If $p$ is a price in whole cents, which of the following could NOT be the result of increasing $p$ by $20\%?$

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Gmat_mission: Legendary Member; Posts: 1622; Joined: Thu Mar 01, 2018 7:22 amFollowed by: 2 members

by Gmat_mission » Thu Nov 19, 2020 11:41 am

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If $p$ is a price in whole cents, which of the following could NOT be the result of increasing $p$ by $20\%?$

A. $\$1.20$
B. $\$1.25$
C. $\$1.38$
D. $\$1.80$
E. $\$2.52$

Answer: B

Source: Princeton Review

Source: Beat The GMAT — Problem Solving | Thu Nov 19, 2020 11:41 am

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Re: If $p$ is a price in whole cents, which of the following could NOT be the result of increasing $p$ by $20\%?$

by Scott@TargetTestPrep » Wed Nov 25, 2020 8:24 am

Gmat_mission wrote: ↑
Thu Nov 19, 2020 11:41 am
If $p$ is a price in whole cents, which of the following could NOT be the result of increasing $p$ by $20\%?$

A. $\$1.20$
B. $\$1.25$
C. $\$1.38$
D. $\$1.80$
E. $\$2.52$

Answer: B

Solution:

Notice that $1.25, or 125 cents, is the only odd number of cents of the answer choices, so we will guess that $1.25 couldn’t be the result of increasing p by 20%. In other words, if p is increased by 20% and the result is $1.25, p couldn’t be a whole number of cents. Let’s show that this is indeed the case.

p x 1.2 = 125

p = 104.167

We see that 104.167 is not a whole number.

Answer: B

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