This is a Data Sufficiency problem from Session 5, Extra Practice HW 3 (Quantitative Strategy). So far, 49.6% of Knewton students have missed it. How would you approach it?

Try it out, then share your answers, questions, and thought processes in the comments below. Remember, if you’re in our GMAT class now, add your teacher name and session to your comment (e.g., Zwelling, MW 1:30).

In 2001, Rembolse Insurance sold 8,250 travel insurance policies in its international division. If 255 of the international division’s policies resulted in a claim, what was the claim rate, i.e. the number of claims per 100 policies, for the domestic division in 2001?

1. In 2001, the overall claim rate for the international and domestic divisions combined was 4.5 claims per 100 policies.
2. In 2001, the domestic division sold 4,550 policies.

[A] Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
[B] Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
[C] BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
[D] EACH statement ALONE is sufficient.
[E] Statements (1) and (2) TOGETHER are NOT sufficient.

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  • Jaspal Saini

    Total International Policies (I)=8250, International Claims (X)=255
    Total Domestic Policies =D, Domestic Claims = Y
    We have to find, Y/D

    Statement 1: Total Claim Rate = 4.5/100, (255+Y)/(8250+D)=4.5/100. Cannot find Y/D, therefore not sufficient.
    Statement 2: D=4550. Not Sufficient.

    Combining 1 and 2, (255+Y)/(8250+4550)=4.5/100. Therefore, we can find Y and thus Y/D. Sufficient. Answer is C.

    • Avtejsawhney

      I’d like to go thorugh the question again.
      We don’t need either of Y or D to get the answer.

    • Avtejsawhney

      I’d like to go thorugh the question again.
      We don’t need either of Y or D to get the answer.

  • Eric

    C?

    • Nguyen

      Answer is C

  • http://twitter.com/Antagonist Felix Sargent

    The hard part here is to figure out what the variables are. That there’s a difference between the international (data provided) and domestic (data required).S_i = 8250 (sold, international)C_i = 255 (claim, international)S_d = ?C_d = ?Question is asking: What is C_d/S_dStatement 1 provides: C_i/S_i + C_d/S_d = 4.5We still have two unknown variables. Insufficient.Statement 2 provides: S_d = 4,550Ignoring statement one, we now have only one unidentifed variable. unfortunately, we have no relationship between international and domestic claims for us to suss out the claim rate. Insufficient.Combining the two answers, with answer _C_ – we can find all unknowns to find the ratio.

    • Anonymous

      Good call, Felix. Identifying the variables can be a big hurdle for this problem. It worked out alright, but your equation from Statement 1 is a little off—4.5 isn’t the sum of the rates, but is rather the combined rate: (C_i + C_d)/(S_i + S_d) = 4.5/100

      • Frank1

        and i feel like people like running like a horse(when many people have said that combined rate not sum of rates).I feel they are not reading input from others before they answer.

      • Frank1

        I want to edit my post.
        Thanks guru
        ……and i feel like though many people have already said that is not sum of invidual rates they are running like a horse which only marches forward looking staight.(They dont seem to consider this fact though many people have already pointed out this thing) and making same assumption to answer the question

  • SandeepV

    I think the Answer is A
    My Views:
    From Question i have International Claim rate…
    now i need just to find domestic Claim rate…
    From 1st statement..I have Int claim rate + Dom. Claim rate=4.5 per 100 policies
    i can find domestic as i can calculate international claim rate per 100…. so Sufficient……

    From 2nd Statement i can only have no. of dom. policies sold no claim can be determined..
    hence Insufficient…..
    (9 AM Monday class Brigidette + Jess Nepom)+Rich Zwelling too :)

  • Jaspal Saini

    It says combined claim rate, which doesn’t mean sum of individual claim rates. So statement 1 is not sufficient.

    • sandeepV

      Yes u r right i just gave it a thought..I am Sorry for My tutors..I have let them down by hurrying up myself in this question :( (

  • Anonymous

    Lets assign below variables before we start.T: Total policies.D: Domestic policies.I: International policies.Tc: Overall Claim rate.Dc: Claim rate for domestic policies.Ic: Claim rate for international policies.————————————Given:I = 8,250.Ic = (255/8250)*100Dc = ?————————Statement 1] Tc = 4.5%Statement 2] D=4,550—————————We know:D + I = TandDc + Ic = Tc—————————From statement 1, we have Tc = 4.5/100and we are given Ic = (255/8250)*100so using equation: Dc + Ic = Tc, we can calculate Dc. So SUFFICIENTFrom statement 2, we have D=4,550then we know, D + I = Twe are given I = 8,250. So we can calculate T.But we still can not find Dc. So INSUFFICIENTSo the answer should be A.

    -Knewton Student
    Steve,Tue/Thu
    6:30-9:30 IST

    • Syapakahaku

      The problem with your answer is to get the overall rate is not as simple as

      Dc + Ic = Tc

      it is…

      Domestic claim + International Claim
      Overall RATE Claim = ______________________________ x 100

      International policies + Domestic Policies

      So, in order to know the domestic claim, we have to know the domestic policies
      and also the overall rate claim. In your solution, you assumed that Overall RATE claim
      is the total of domestic and international claim, which is not.

      That’s my opinion. Thanks.
      —————————
      Indonesia Student

    • Michmobi

      I disagree with the equation Dc+Ic=Tc. I think the equation for Tc should be Tc=(Cd+Ci)/(D+I) where Cd and Ci are the number of claims for domestic and international divisions, respectively. You cannot simply add fractions with different denominators (i.e. D and I). Think of it as a weighted average where both rates should not have equal value if there are more claims in one division than another. Try plugging in numbers where D does not equal I.

    • Sumedha

      ohh wait Steve….
      You missed something there Please check Dc+Ic is NOT EQUAL to Tc.

      and to prove that lets take
      D=100
      I=100
      so T=D+I=100+100=200.
      now if
      International polices claimed are=4 (its not a claim rate)
      and Domestic polices claimed are =4 (its not a claim rate)

      so you get Dc=(4/100)*100=4
      Similarly Ic=(4/100)*100=4
      so Dc+Ic=4+4=8

      and if we calculate Tc =((4+4)/(100+100))*100=(8/200)*100=4

      so Dc+Ic IS NOT EQUAL TO Tc

      The correct answer for the above question is C (both statements together are sufficient)

  • Mankaran

    the answer is c…….

  • NSA

    Answer is A

  • Sreepuram Prashanth

    Ans is C

  • lionslion

    Answer: A

    Statement 1 provides the claim rate for both domestic and International policies.

    from the question we can get the international division policies claim rate. so with information from statement 1 we can get the claim rate for domestic division policies.

    • Anonymous

      Careful – the equation Statement 1 gives us is 4.5 = 100(Ic + Dc)/(Ip + Dp), where Ic and Dc are the numbers of international and domestic claims, respectively, and Ip and Dp are the numbers international and domestic policies sold, respectively. There is no way to solve for Dc/Dp, which we need for the domestic claim rate.

  • Abai150

    First we can calculate claim rate for int. division. Then using information from statement 1 we can figure out claim rate for domestic division. Statement 2 is insufficient.
    So A is correct.

  • Ruan

    It is C for the following reasons :
    Statement 1 tell you about the combined (average) claim rate, so while you have the claim rate of international claims (255/8250 X 100) you would need to know the number of domestic claims to obtain the domestic claim rate from from the averages. proof below:

    tC = Total claims
    dC = Domestic claims
    iC = International claims
    tC = dC + iC

    tP = Total Policies
    dP = Domestic Policies
    iP = International Policies
    tP = dP + iP

    aC = Average combined claim
    aI = Average International claim
    aD = Average Domestic claim
    aC != (aI+aD/2)

    aC = tC/tP = (dC+iC)/(dP+iP)
    aC is known = 0.045 (4.5/100)
    iC is known = 255
    iP is known = 8,250
    dP is known = 4,550
    dC is not known and is asked for..

    therefore to have one variable in the equation to solve, you need both statement 1 (providing aC) and statement 2 (providing dP)

  • kansi

    C.. Both together would be sufficient.

  • http://twitter.com/carlopacot Carlo Pacot

    The answer is B.

  • Luca_dipalo

    For me is C
    The combined rate equals: Tc = (Claims_I+Claims_D) / (TI_I+TI_D)
    Tc /= (Claims_I / TI_I) + (Claims_D / TI_D)

    Or not?

  • Luca_dipalo

    For me is C
    The combined rate equals: Tc = (Claims_I+Claims_D) / (TI_I+TI_D)
    Tc /= (Claims_I / TI_I) + (Claims_D / TI_D)

    Or not?

  • AD

    C ..pretty sure.

  • AD

    C ..pretty sure.

  • Mmarshall

    E – because data required to calculate is based on international claims, no domestic(specifically) claim information is made available, therefore no conclusion can be made about the domestic claim rate per 100 policies.

  • seshao7

    ans : c

  • Asrarqamar

    e ?

  • Siva

    Answer C

  • Dp

    answer a

  • vciura

    B?

  • Manali Sharma

    The asnwer should be “C”.
    The overall claim rate is 4.5 which is basically the average of international and domestic policies.

    Statement 1 alone does not help to find the exact rate for domestic market.
    Statement 2 alone also does not help.

    When we combine both statements together, we can calculate the clam rate for domestic market as below:
    Total number of insurance sold=8250+4550=12800
    Total claim rate=4.5, therefore total number of claims sold=12800*4.5/100=576
    Therefore, total number of claims for domestic market=576-255=321
    Now, we can easiy calculate the domestic claim rate=321/4550*100

    Hence, correct answer is C

  • CONG

    Answer is E.

    1) doesn’t give enough info to calculate international claim rate
    2) we don’t need domestic info

  • Anu

    the answer is A
    overall claim rate is {c(d)+c(i)}/{s(d)+s(i)}*100=4.5,
    have to calculate c(d)/s(d)*100
    we have s(i) and c(i), plugging in these to the equation above wud give us the ratio c(d)/s(d) and hence, we can find the answer.

    While statement 2, only gives us s(d) which is not enuff.

  • Orlee

    The first point of action is to assign variables:
    CD = domestic claims
    CI = international claims
    PD = domestic insurance policies
    PI = international insurance policies

    i) This tells us that the overal claim rate was 4.5 per 100

    This means that [(CD+CI)/(PD+PI)] =4.5/100
    We know some of these values already from the stem. So, filling in we get:
    (CD+255)/(PD+8250)=(4.5/100)
    The problem is that by solving this solution we are still left with two unknowns: CD and PD
    Therefore NOT SUFFICIENT.

    ii) From this, we know that the domestic division sold 4550 policies.
    So, using the formula from (i) we now have the following formula:
    [(CD+255)/(4500+8250)]=????
    In order to find the domestic rate, we need CD/PD. However, (ii) doesn’t allow us to figure out what CD is.
    Therefore, NOT SUFFICIENT

    (i) & (ii) together?
    We have [(255+CD)/(4550+8250)]=4.5/100 With this information, we can determine CD. With a value for CD, we can determine CD/PD. From this equation, we get that CD=321
    and CD/PD=321/4550

    THEREFORE, the answer is C

  • Avtejsawhney

    Answer is option A.

    From the question we can calculate the number of claims per 100 policies for the international division. now add this to no. of claims per 100 policies for the domestic division and equate it to 4.5 to get the answer.

  • VP

    C….without a doubt..

  • sandeep

    C – My Answer.

    With option A, we cannot breakup the claim rate between International and Domestic divisions.

  • Vamsi Emeperor

    Answer is C

  • aisha

    answer is A

  • aisha

    answer is C
    total # of insurance sold
    intl div + domestic div 8250 +4550=13800
    intl claims=255
    plug on the 1st equation
    int claims+dom claim / =4.5%(255+x/8250+dom sales =4.5
    8250 +domestic sales
    scratch choice A&D it didnt enough information
    equation 2
    total sales 8250+4550=13800
    13800 =100%
    X =4.0%
    X(Total claim =621=4.5%
    dom claims =621-255=366
    366 = how much % of 13800
    366/13800 *100 =2.7
    int claim=4.5-2.7=1.8
    that means the answer is choice C

  • Danny

    A – and who needs a formula for this question? Claim rate for Int’l is 255/8250=3, so claim rate for Dom is 4.5-3=1.5. B neither helps, nor stands on its own to solve the problem.

  • Walter B

    E appears to be correct

  • Contact

    I think C is the answer.
    To all those who answer A, I think the point that you are missing in your calculation is that the combined claim rate must be (iClaims + dClaims/iPolicies + dPolicies)x100. This accurately weights each divisions number of policies and claims in the calculation of the overall claim rate.

    • Contact

      If I am missing something, I would love for one of the A answerers to explain why their answer is correct.

  • Marcatack

    Answer is C

  • Marcatack

    The claim rate for total policies = 4.5%there fore you need the total number of policies which is equal to 12800. this means there is 576 total claims.
    We know that there were 255 claims for the INT. DIV. Therefore we now know that Domestic Claims is 321 of 4550 total or 7.1%

    Statement 1 – Insufficient
    Statement 2 – Insufficient
    Both – Sufficient.

  • Suren

    Answer:- C

  • Christianvela60

    Answer is A:

    Sold Claim Rate
    International 8250 255 3,091
    Domestic X Y [(X/100)*Y]
    Total 8250+X 255+Y 4,5

    Two Variables & Two Equations:

    (I) [(850+X)/100]*(255+Y) = 4,5
    (II) {(3,091*8250)+[(x^2)*Y/100]} / (8250+X) = 4,5 (Rate by weighted average)

    Solving these equations is suficient to answer domestic claim rate (XY/100)

    B is alone is insuficient because there is no information concerning domestic o total claims

  • Christianvela60

    Sold Claim Rate
    8250 255 3,091 (international)
    X Y [(X/100)*Y] (domestic)
    8250+X 255+Y 4,5 (total)

  • Guptadeepali

    Answer is A.

  • Eli_m42

    B is correct i think.

  • babydoll

    it is C. You can’t know the rate if you don’t know proportion, i.e. you have to know the number of of issued insurances in both sections….I’m pretty sure on this one..

  • Vinamra Gharat

    well, Answer is “A”, was oral question. You don’t have to solve this question. Since combined rate and international rate are given, we can easily get domestic rate. A simple x,y problem where x and combined percentage of xy is given. We need to find y!

  • Barbozareric

    Idon´t need any equation, just thinking.
    Answer c

  • mudit

    answer is c
    the question provides the information only for the international sector, the first statement provides information about the total claims, while the second provides information about the no of domestic policies sold… how can u find the claims per 100 fr domestic division without knowledge of the total claims and also the total no of domestic policies sold… we have to find the total policies sold, multiply it by (4.5/100) to get the total claims… subtract 255 from it to get the required result….

    C is clearly the answer

  • Anonymous

    There’s some great discussion going on here! For those of you choosing answer choice A, notice that the total number of claims includes the number of international claims (we can call that Ic) and the number of domestic claims (we can call that Dc). Similarly, the total number of policies includes both international and domestic, Ip and Dp. The overall claim rate is equal to the total number of claims divided by the total number of policies (and that whole expression multiplied by 100). So, total claim rate = 100(Ic + Dc)/(Ip + Dp). With Statement 1, we have one equation with two unknowns, Dc and Dp.

    To the current Knewton students out there, this question will as usual be discussed during the two upcoming office hours sessions—Saturday, November 6, at 11am (EST), and Wednesday, November 10, at 8pm (EST).

  • Samiran

    The should be C

    Combining the qs stem with options 1 and 2 the eqn becomes

    4.5/100 = ((255 + R(4,550 )/(8,250 + 4,550 )) => R = ?

  • Mia

    For those who still believe the answer is (A), think about the problem this way:

    The claim “rate” is the number of claims filed per policy sold, expressed as a percentage (in the prompt they say “per 100 claims” to essentially tell you that). Remember that x/100 is simply x%. Same idea here.

    So, think about average rate problems. What is the number one rule with average rate problems? DON’T combine rates, work with the raw data.

    Example: If John walks the first half of his route at 2mph and the second half at 5 mph, and you want to find his AVG RATE, you do NOT add 2+5 and divide by 2. You MUST take the TOTAL NUMBER of miles traveled and divide it by his total TIME (which you will derive from the original rates) to find his average rate for the entire route.

    Similarly, in the problem we are discussing here, you cannot simply add the two rates and put them over 100. You MUST add up the TOTAL NUMBER of CLAIMS FILED (domestic+international) and divide by the total number of policies sold (domestic+international) to find their combined rate. (It’s like a weighted average in many ways.) Once you do that, you can express your result as a percent (%) to show that it is “per 100″ claims.

    But, as you know, you will not have to do all this math, you just have to recognize that you will need to know the exact NUMBER of domestic claims to solve this problem.

    The answer would therefore be (C).

  • Swaptrip

    The answer would be “E” both statements are insufficient to answer the question. suppose total number of international policies sold that year is x and total claims in domestic division-y.Then using both statements 1 and 2 we can write:
    4.5/100 = (y+450)/(x+4550)

    We have two variables and 1 equation, so we cannot solve using both the statements hence E

  • Swaptrip

    I don’t think that total travel policies sold can be assumed as total policies.

    • Anonymous

      Great point. The tricky thing is that this does occasionally occur on the GMAT. So, in creating our material here at Knewton, we have to include a certain number of questions with ambiguity in order to accurately reproduce the experience of the test. I sometimes want to argue with the test-maker, particularly on critical reasoning questions that rely too heavily on the word “best” (eg, which of the following best supports…). When this comes up on a question like this data sufficiency problem, you have to decide whether you think the test-maker is testing your ability to make subtle distinctions or is just being too loose in its language.

      Here, the problem does not describe the existence of multiple types of policies—it refers to travel policies and then to policies more generally. Since the statements do not hint at the issue of whether or not there are other types of policies, we are forced to make a leap and assume that travel policies and policies are interchangeable.

  • Vidyasagar

    E is my answer….and it’s a cheap answer…coz the question seems ambiguous

    “travel insurance” policies (not equal to) all insurance policies….hence E…delete the word travel and the answer is C…..will any expert give us the OA?

    • Anonymous

      Great point. The tricky thing is that this does occasionally occur on the GMAT. So, in creating our material here at Knewton, we have to include a certain number of questions with ambiguity in order to accurately reproduce the experience of the test. I sometimes want to argue with the test-maker, particularly on critical reasoning questions that rely too heavily on the word “best” (eg, which of the following best supports…). When this comes up on a question like this data sufficiency problem, you have to decide whether you think the test-maker is testing your ability to make subtle distinctions or is just being too loose in its language.

      Here, the problem does not describe the existence of multiple types of policies—it refers to travel policies and then to policies more generally. Since the statements do not hint at the issue of whether or not there are other types of policies, we are forced to make a leap and assume that travel policies and policies are interchangeable.

  • Fdecazaux

    My answer is A.
    We know the claim rate for international policies (255 / 8250).
    – A gives the total claim rate for both international and domestic policies so it allows to calculate by difference the claim rate for domestic policies.
    – B gives the number of domestic policies, but gives no indication about the number of claims

    A is sufficient.
    I think the difficulty of the question is that B can be combined to A to find the answer, though A is sufficient alone, and B is not sufficient.

  • Preeti

    I believe that the answer is C

  • Anonymous

    Answer is A… take it as mixture and allegation problem total proportion known of one of the mixture.. second mixture can be deduced

  • Ndokpascaline

    Answer C

  • Srdjan

    C) Because 4.5 claims is a weighted average of both divisions, we need both the number of policies sold domestically and the information that 4.5 claims per 100 policies were the overall average.

  • Paulamidas 16

    I go with option A. Explanation below:

    Ic + Dc = Overall claim rate,
    (255/8250)x100 + Dc= 4.5, we can solve for Dc. So A is sufficient

    Option B gives us the total no.of Domestic Insurance but not the no. of claims. So we cannot solve for Dc, so B insufficient.

  • Naveen

    The 2 schools of thought that I’m seeing comes from the confusion of not understanding “rate” in this context. Note that, rates CAN be added in a work-related problem but CANNOT be done here. Here is why:

    1) If “Rate” calculation involves “Time”, then Combined rate = Sum of Individual rates.

    2) If “Rate” calculation does NOT involve “Time”, then Combined rate != Sum of Individual rates.

    Example-1:
    ————
    If Susan takes “x” hours to paint “y” houses and Leslie takes “a” hours to paint “b” houses, then Combined rate = (y/x) + (b/a). ADD the rates, because individual “rate” uses time (x or y).

    Example-2:
    ————
    If Susan can post “x” letters from a box of “y” letters on a given day and Leslie can post “a” letters from a box of “b” letters on the same day, then Combined rate != Sum of individual rates. DO NOT ADD the rates because “rate” calculation in this context does NOT depend on time.

    Susan’s rate = x/y
    Leslie’s rate = a/b
    Combined rate = (x+a) / (y+b)

    Hope that helps.
    -Knewton student
    Adam, Tue/Thu
    8pm – 11pm PST

  • Daniel

    One needs boths statements to form a valid argument
    Hence both statement together are sufficient, but not mutually exclussive.
    4550=X
    (8250-4550)=4.5
    X=5.5
    Answer. C

  • Frank1

    Sample A total=8250 value=225
    Sample B total=x value=y (y/x)x100

    Total A+B total=8250+x value=225+y ((225+y)/(8250+x) X 100)

    Question is
    (y/x)x100=?

    St 1
    1. In 2001, the overall claim rate for the international and domestic divisions combined was 4.5 claims per 100 policies.
    ((225+y)/(8250+x) X 100) =4.5
    dont feel it is sufficient

    St 2
    2. In 2001, the domestic division sold 4,550 policies
    X=4550
    No way to get Y so insufficent

    1+2 seems to be sufficente
    when we put y in eq from st 1 we get y hence y/x * 100

    I think its C
    I think its like if speed from A-B is 9km/h and B-C is 6km/hr speed for A-C is not 9+6/2
    same with percent here i guess

    • Frank1

      edit:(no way to edit so) …these lines should read….
      Question is
      (y/x)*100=?
      ……….
      when we put value of x from st 2 in eq from st 1 we get y hence y/x * 100

  • K Ravikumar

    Answer is C – Both statemetns together are sufficient

  • Pierre

    Technically, statement (1) is what tells us the combined rate of international and domestic insurance policies resulted in claim. without it, the domestic rate could be anything between 0 and 100, and we wouldn’t know the total international plus domestic sold. Statement (2) only tells us the total domestic sold with no limit on how many were resulted in a claim. Thus, both statement are needed in order to find the correct answer. therefore, C is the correct answer.

  • Nks_heaven

    Option [A] is my answer

  • Sid

    its a tricky question no wonder so many of us got bowld.

    let try to understand the question with some easy data

    suppose for international we have total (It)100 policies were sold and (Ic)25 were claimed
    and (Dt)50 total Domestic policies sold and (Dc) 25 Domestic claim
    So international claim rate is 25% and domestic claim rate 50%
    so 25% + 50% =75 % total claim rate ,but is that the real picture ?
    we know that total claim rate will be 25+25/100+50=33.3%
    this inconsistancy is resulting from the fact that we really dont know the size of domestic claim. If the size of domestic and international claims had been same we could have got the answer but we have no information about it.

    according to statement 1

    255/8250*100 + (Dc/Dt)*100 = 4.5 /100 (1)

    4.5=(255+Dc)/(8250+Dt) (2)

    from (1) and (2)

    (255/8250 )*100 + (Dc/Dt)*100=(255+Dc)/(8250+Dt)*100
    2 variables 1 equation (A insufficient)

    statement 2 give us Dt=4,550

    B insufficient we can tell it by face of it.

    Now,if we substitute the value of Dt in above equation we get 1 variable 1 equation .
    Bingo! We have our answer C.

    Siddhartha Singh ( teacher -Rich Zwelling , my batch(19th Nov) is over now SAT/SUN(8:30pm)

  • Yalqayem

    Answer is A

  • Reinaa2

    my answer is a “c” combined, is very similar to others I have already studied.  It is a good question for a beginner, for somebody who has studied advanced material should expect a more challenging question.  

  • Sumeet Sethi

    The answer is [A]
    Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

  • enigmatic

    Answer is B

  • Matt091586

    Rate INT = 255/8250
    Rate DOM = ?

    Statement 1 : 255/8250 + y = 4.5/100
     -> 255/8250 gives a percentage
     -> 4.5/100 gives a percentage
     -> y = (255/8250) + (4.5/100)
     -> Result is rate for DOM claims

    Statement 2 : Given excerpt does not provide any relevant information to solve for DOM claims. In other words, we are left with :
     -> x/4550 = y

    Answer is A.

    • Kartik

      Your equation seems to be incorrect.
      Overall Claims Rate can be expressed as: (Total Claims / Total Sales)* 100
      Accordingly it will be [(255+x)/(8250+y)]*100 = 4.5/100
      Hence value of x is required from Statement 2 to solve further.
      This is why A is a tricky choice but not necessarily the right answer. 

  • Matt091586

    Woops…

    Statement 1 equation to solve answer should be:
     -> y = (255/8250) – (4.5/100)

  • Binsnitin11

    Ans should b A cauz a gives combined claim rate for int. & domestic ,and question gives the rate of int. So domestic can easily calculated by stement 1
    but statement 2 gives only no of domestic policy not about any link to the question
    thus A

    • http://www.knewton.com Knewton Team

       Hey Binsnitin11, check out the explanation above — hopefully that will explain why C is the right answer. Let us know if you still have questions!

      • Guest

         As per your calculations, Domestic rate = 7.05 or something. But the problem gives say total rate = 4.5. How can this be possible? I would say A is correct

  • http://kamalblogs.wordpress.com/ casperkamal

    Assume X = Total returned domestic claims
    Y = Total domestic claims, 8250 = International total, 255 = International claim
    1. tells us that 255+x/8250+y = 4.5 There are two variables impossible to solve2. 255+x/8250+4550 = ? Gives the total value of domestic claims but not the result
    3.255+x/8250+4550 = 4.5 Yes we can find x 

    So IMO,  (C) is the answer … Knewton experts please comment

    • http://www.knewton.com Knewton Team

      Nice work casperkamal! C is correct. Check out the explanation above. 

  • http://www.knewton.com Knewton Team

    Hey guys, here is the explanation:

    We need to determine the percentage of policies in the domestic division
    that resulted in claims in 2001. To find this percentage, we will need to
    determine both the value of x, the number of policies sold in the domestic
    division, and the value of y, the number of policies sold in the domestic
    division that resulted in claims. Alternatively, if the value of x/y can be
    determined, converting that fraction to a percentage will yield the percentage
    of domestic policies that resulted in claims. We know that the international
    division sold 8,250 policies, 255 of which resulted in a claim.

    Statement 1 says that the claim rate for both divisions combined was 4.5/100.
    It is tempting to think that this is sufficient, since we have both the
    international rate and the combined rate. But notice that the actual size of
    the domestic division’s business is very important. If they sell a lot, say,
    500,000 policies per year, then the 255 claims out of 8,250 policies from the
    international division will barely have an effect on the overall claim rate,
    meaning that the domestic rate will be very close to 4.5, the combined rate. On
    the other hand, if the domestic division is small and sells only 1 policy in
    2001, then their rate could either be 0 or 100 claims per 100 policies (which would
    be estimated figures) and yet that rate would have almost no effect on the
    combined rate.

    So, we set up a proportion with total claims in the numerator and total
    policies in the denominator: (255 + y)/(8250 +x) = 4.5/100. Cross multiply:
    25500 + 100y = 37125 + 4.5x, which simplifies to 11625=100y – 4.5x. This
    equation cannot be solved for either variable, nor can it be solved for the
    fraction x/y. Statement 1 is NOT sufficient to answer the question. Eliminate
    answer choices A and D. The correct answer choice must be B, C, or E.

    Statement 2 says that the domestic division sold 4,550 policies: x=4550.
    However, it gives no information about the number of policies sold in the
    domestic division that resulted in claims. Thus, statement 2 is NOT sufficient
    to answer the question. Eliminate answer choice B. The correct answer
    choice is either C or E.

    Taken together, the statements give us two equations: 11625 and 100y – 4.5x
    and x =4550. We can plug in 4550 for x and solve for y. Then, since we know
    both x and y, we can determine y/x and convert it to a percentage. Together,
    the statements are sufficient.

    Answer choice C is correct.
     

  • Shingik

    C is the answer. This sort of looks like  a weighted averages problem. so in order to answer the question you need to know what effect or weight the total number of both division will have.

  • Dilinox

    Hey guys, I am a Software Engineer and use a simple algorithm to solve Data Sufficiency Questions.
    Here is the algorithm.

    Evaluate Statement (1)
     if (Statement (1) is Sufficient)
        Answer is either A or D
     else
        Answer is either B, C, or D
     end

    So for this problem, since Statement (1) is sufficient, then the answer is between A or D
    CR(total) = CR(Domestic Division) + CR(International Division)
    CR(total)= 4.5/100 = 0.045
    CR(International Division) = 255/8250=0.030909091
    CR(International Division) = 0.045 – 0.030909091 = 0.014090909 ~ 1.4/100

    Statement (2) is not sufficent. Why?
    CR(total) = unknown
    CR(Domestic Division) = unknown/CR(total) = Not given
    So you have 2 unknowns in one equation = Can’t solve this algebraically, you need two equations instead.
    CR(International Division) = given

    So answer is A..

    • guest

      you cannot add rates as 2+2=4 .. you can add the number of claims as 2+2=4.
      Check the official explanation.

    • Jarrod

      I think your algorithm makes sense but your understanding of the claim rate is flawed…

  • Ell

    If we can calculate the international rate using the Total and Claims, and we only have the combined international and domestic rates, we don’t have enough information. 

    However, when we find out the domestic total we can add domestic and international totals (12800) and multiply by the rate 4.5 per 100 to get the total number of claims (576)

    From here we can subtract the claims we know to be international (255) and divide the domestic claims (321) by the domestic total (4550) to get the domestic rate.

    My question: is there a less math intensive way to do this?
    Thanks!