Bunuel wrote:

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

Using answer choices is quick. Steps:

1) Start: J has 40% more than P. (J = 1.4P)

2) P, start #? Find from #1

3) Then J, end: (J - 45)

4) And P, end: (P + 45)

5) At the end, does P have 10% more = 1.1J?

One more step. To begin, J = 1.4P. There is a factor of 7, which often is not a "nice" number.

Convert:

\(1.4=\frac{14}{10}=\frac{7}{5}\)Start:

\(J=\frac{7}{5}P\) which means that

\(P=\frac{5}{7}J\) To find a benchmark, start with (C)J, start: 200

P, start:

\(\frac{5}{7}J\)P, start:

\(\frac{5}{7}*(200)\)STOP. 200 is not divisible by 7

J's original # of stamps must be divisible by 7

Eliminate C and D Not divisible by 7. Other options? Quick math: (A) 140 = (7 * 20).

(B) 175 = (7 * 25). (E) 245 = (7 * 35) Keep all

Lower and upper limits are A and E. Test one of them. C was no help

Try (A) 140 J, start: 140

P start:

\(P=(\frac{5}{7}*J)=(\frac{5}{7}*140)=100=P\)P start: 100

J, final: (140 - 45) = 95

P, final: (100 + 45) = 145

Does P now have "10% more than J" =

\(1.1J\)?

\(\frac{P}{J}=\frac{145}{95}\approx\frac{150}{100}\approx{\frac{3}{2}}=1.5\) REJECT

\(P\approx1.5J\) is much greater than

\(P=1.1J\)J's original # must be greater so that (J - 45) has a smaller impact. Increase J's base by a lot

E) 245P, start:

\(\frac{5}{7}J=P\)P, start:

\(\frac{5}{7}*(200)=175\)J, final: (245 - 45) = 200

P, final: (175 + 45) = 220

Is P now equal to 1.1 J?

\(\frac{P}{J}=\frac{220}{200}=\frac{11}{10}=1.1\)That's a match.

Answer E