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
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