A casino uses chips in $5 and $7 denominations only. Which of the following amounts CANNOT be paid out using these chips

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A casino uses chips in $5 and $7 denominations only. Which of the following amounts CANNOT be paid out using these chips?

(A) $31
(B) $29
(C) $26
(D) $23
(E) $21

Answer: D
Source: Manhattan prep

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BTGModeratorVI wrote:
Thu Dec 03, 2020 2:44 pm
A casino uses chips in $5 and $7 denominations only. Which of the following amounts CANNOT be paid out using these chips?

(A) $31
(B) $29
(C) $26
(D) $23
(E) $21

Answer: D
Solution:

In order to determine the correct answer, we need to check every answer choice (keep in mind that we are looking for the dollar amount that we CANNOT be paid out using the chips).

A) $31

Since two $5 and three $7 chips will make $31, this is not the correct answer.

B) $29

Since three $5 and two $7 chips will make $29, this is not the correct answer.

C) $26

Since one $5 and three $7 chips will make $26, this is not the correct answer.

We are now left with choices D and E. If we look at choice E, three $7 chips will make $21. Therefore, it’s not the correct answer. This leaves us with only D as the correct answer.

Answer: D

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BTGModeratorVI wrote:
Thu Dec 03, 2020 2:44 pm
A casino uses chips in $5 and $7 denominations only. Which of the following amounts CANNOT be paid out using these chips?

(A) $31
(B) $29
(C) $26
(D) $23
(E) $21

Answer: D
Source: Manhattan prep
We can quickly get the answer by eliminating four of the answer choices

(A) $31 = 2($5) + 3($7). ELIMINATE A
(B) $29 = 3($5) + 2($7). ELIMINATE B
(C) $26 = 1($5) + 3($7). ELIMINATE C
(D) $23 =
(E) $21 = 3($7). ELIMINATE E

Answer: D

Cheers,
Brent
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