Quote:
Jennifer has 40% more stamps than Peter. However, if she gives 45 of her stamps to Peter, then Peter will have 10 % more stamps than Jennifer. How many stamps did Jennifer begin with?
(A) 140
(B) 175
(C) 200
(D) 220
(E) 245
If struggling with the algebraic approach, note that in any GRE problem seeking one specific numeric value with the choices in ascending or descending numeric value and the phrase "how many" present, it is likely that a backsolving approach can be successful. Since the other explanations in this thread have more than adequately explained the algebraic method, let's take a look at the backsolving alternative.
List the choices for the problem as seen below.
Jennifer Stamps Beginninga) 140
b) 175
c) 200
d) 220
e) 245
Then, eliminate any logically impossible choices by considering the steps of the problem. Since the first step of the problem states that Jennifer's number of stamps is 40% more than Peter to begin we know that to find Peter's number of stamps we must divide Jennifer's stamps by 1.4 or 7/5, which logically means that the correct choice must be divisible by 5 and 7 to result in whole number stamp values. Therefore, confidently eliminate choices C & D which are not divisible by 7. This leave choices A, B, and E, so take the middle remaining choice B and work through the constraints of the problem using columns as follows:
Jennifer's Stamps Beginning | Peter Stamps Beginning | J Stamps - 45 | P Stamps +45 | Does P Have 10% More?||||||||
b) 175 |||||||||||||||
175 ÷ 1.4 = 125 |||
175 - 45 = 130 |
125 + 45 = 170 ||
No (Too Many) Because choice B is too low of a start for Jennifer and only choice E remains a logical possibility during the exam you should immediately select E. However, let's look at the column set up for the choice to confirm that it is indeed correct.
Jennifer's Stamps Beginning | Peter Stamps Beginning | J Stamps - 45 | P Stamps +45 | Does P Have 10% More?|||||||||
e) 245 ||||||||||||||
245 ÷ 1.4 = 175 ||||
245 - 45 = 200 |
175 + 45 = 220 ||||
Yes!
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