GMAT Club Legend
Joined: 03 Oct 2013
Affiliations: CrackVerbal
Posts: 4946
Given Kudos: 215
Location: India
Re: In the set S of consecutive integers from 1 to 10, inclusive, D is the
[#permalink]
20 Mar 2020, 04:33
Set S = {1,2,3,4,5,6,7,8,9,10}, set D = {1,3,5,7,9}, set M = {2,3,5,7} and set Q = {1,4,9}.
d is an element of D implies d is an odd integer.
m is an element of M implies m is prime. Note that m can be either odd or even but m cannot be a fraction.
q is an element of Q, therefore q is a perfect square.
We are trying to establish which options COULD BE true. Therefore, we just need one case which can make an option TRUE, once.
Let’s start with option A. Option A says d= √mq.
Since d is an integer, this means that mq should be a perfect square. But, on close observation, none of the values mq can give us a perfect square. Therefore, option A is definitely false under the given conditions. Option A can be eliminated.
Option B says d = q/m. If we take q = 9 and m = 3, d=3. So, d=q/m could be true. Let’s hold on to answer option B.
Option C says m=q. This is definitely false. Option C can be eliminated.
Option D says q=\(\frac{m}{d^2}\). q is a perfect square. Since \(d^2\) will be much larger than m in most cases (except when d=1, but taking the case of d=1 is pointless since we will not get a perfect square anyways) and so m/d^2 will always be a fraction. A fraction cannot be a perfect square. Option D is definitely false. Option D can be eliminated.
Option E says q = √dm. Since q has to be 1 or 4 or 9, dm has to be 1 or 16 or 81. None of the combinations of dm will give us any of the above values. Option E is definitely false. Option E can be eliminated.
The correct answer option HAS to be B.
At the outset, although this question appears to be an easy one, it does take time to dig deeper, test out cases and understand the underlying concept to negate the options. So, you should be wary of such questions that look simple but are really not. You should also be careful in not trying out too many values in this question, else you’ll get swamped by them.
Hope that helps!