Two hundred multiples of seven are chosen at random, and 300 multiples

Question

Two hundred multiples of seven are chosen at random, and 300 multiples of eight are chosen at random. Approximately what percentage of the 500 selected numbers are odd?

A. 20%
B. 25%
C. 40%
D. 50%
E. 80%

persist99 · Answer

--> Multiples of 7 are 7, 14, 21, 28, 35, 42....

Out of first 4 multiples, 2 are odd; out of first 6 multiples, 3 are odd.

So approx. 50 % of the 200 multiples are odd i.e 100 multiples.

--> Similalrly, for 8 multiples are:8,16,24...

All are even so 0 % are odd.

Total odd= (100+0)/(200+300)= 100/500=(1/5) = 20% >>>>My answer A

GMATinsight · Answer

Two hundred multiples of seven will have 100 even and 100 odd numbers

300 multiples of eight will have ALL even (being multiple of 8)

Probability of number selected being odd = Total Odd Numbers / Total available numbers 
Probability = 100/500 = 0.2 = 20%

Answer: Option A

Rohit_842 · Answer

In order for A to be the right answer one must assume there are exactly 100 even and 100 odd multiples of 7. Correct answer could be C too if you assume all 200 are odd multiples. Kindly help if I'm missing something  Bunuel

Bunuel · Answer

We are randomly choosing 200 multiples of seven from  infinite number  of multiples of seven. Since half of all multiples of seven are odd and the other half are even, we can expect  approximately  100 odd and 100 even among the selected 200.

Since all multiples of 8 are even, the total set of 500 numbers will consist of  approximately  100 odd and 400 even.

Thus, the probability of selecting an odd number is 100/500 = 1/5 = 20%.

AbhishekP220108 · Answer

Bunuel , I don't agree. If you are expecting approximately 100 odd and 100 even, then I can assume 125 odd and 75 even multiples of 7, since it is given 200 multiples of seven, not just the first 200 multiples of seven. As far as I know, GMAT options are not ambiguous. Here, everyone is assuming that there are 100 odd and 100 even. What if all 200 are odd multiples? Then the answer can also be 40% also. Please check once

Bunuel · Answer

This is not an official question, and the wording could be improved. However, the solution you quoted is correct. The distribution of odd and even multiples of 7 is expected to be 50-50, so 100 odd and 100 even. We are randomly picking 200 multiples of 7, so it’s expected to get 100 odd and 100 even. While it’s possible to get 125 odd and 75 even numbers, it’s less likely than getting 100 odd and 100 even. It’s also possible, though much less likely, to pick only odd multiples or only even multiples of 7. But the reasonable assumption is a 50-50 split.

Two hundred multiples of seven are chosen at random, and 300 multiples

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