Baten80 wrote:A has $18 more than what B & C together would have had if both B and C had 1/4 of what A has. How much does A have?
(A) 20
(B) 48
(C) 32
(D) 36
(E) 40
We can certainly solve via algebra, but backsolving is another great approach to take to word problems with numbers in the answer choices.
One thing that's a bit odd about this question is the ordering of the choices - on the actual GMAT, answers are almost always arranged in ascending or descending order. Here they're not (what's the source?), but we can fix that by a quick rearrangement on our scrap paper:
A) 20
C) 32
D) 36
E) 40
B) 48
Now that we have them in order, let's start with either the 2nd or the 4th choice. 40 looks like a nice easy number with which to work, so let's start there.
If A has $40, then each of B and C has $10 (1/4 of 40); combined, B and C have $20.
Is $40 $18 more than $20? NO - therefore, $40 is incorrect.
Now we ask ourselves, is $40 too much or not enough? Since the gap is more than $18, $40 is too much; accordingly, we eliminate $40 and $48 (that's why we put the answers in order!).
3 choices remaining, test the middle one, $32.
If A has $32, then each of B and C has $8 (1/4 of 32); combined, B and C have $16.
Is $32 $18 more than $16? NO - therefore, $32 is incorrect.
Now we note that the gap is too small; accordingly, we need a bigger answer - eliminate $20 and $32.
Only $36 remains - absolutely no need to test it, choose (D).
