Jennifer has 40% more stamps than Peter. However, if she gives 45 of

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) 245
P, 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

since j = 7/5 p
p = 5/7 j
so options has to be multiple of 7 so 2 options are rejected check rest 3 options

How could you calculate 94.5/0.54 mentally or without a calculator? JeffTargetTestPrep

Lets say, Peter has x stamps and so, Jennifer has 1.4 *x stamps. When, 1.4 *x - 45, then (x + 45) is 110% of 1.4 *x - 45. So, x + 45 = 1.1 (1.4 x -45) , or, 1.54 x - 49.5 , 0. 54 x = 94.5 , x = 1050/6 = 175.
Jennifer had 175 + 70 = 245 stamps.
E is the answer.

Multiply both numerator and denominator by 100.

It will give you 9450/54. Then divide.

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