thanks

Peter (X+45)-Jennifer(1.4X-45)=10% of Jennifer (1.4X-45)
So, X=175.
Jennifer=1.4*175=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 Beginning
a) 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!

Amazing explanation.

I have exhausted the kudos for you Sir, though.

regards

Thanks, sir! Hopefully just getting started as a contributor here at GRE Prep Club!!

That's a smart approach, but I think you missed out B. 175/1.4 = 125.

Another quick approach

If we look at the answer choices then only 245 and 140 would give an integer when divided by 1.4 - number of stamps that peter started out with. Since number of stamps can only be an integer value rest all choices are out.

140 - J starting stamps..........therefore 100 - P starting stamps
If J gives 45 then
J = 95 and P = 145........10% of J is 9.5 again out because not an integer.

245 - J starting stamps.......therefore 175 - P starting stamps
If J gives 45 then
J = 200 stamps and P = 220 which is 10% more of J........also 10% of J at this point is 20 which is possible.

Cheers.

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