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11 Mar 2020, 03:26
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
15%
(low)
Question Stats:
81% (01:31) correct
19%
(01:33)
wrong
based on 162
sessions
History
Date
Time
Result
Not Attempted Yet
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
(A) $31
(B) $29
(C) $26
(D) $23
(E) $21
11 Mar 2020, 06:23
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Bunuel
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
General Discussion
11 Mar 2020, 23:06
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The amounts paid out here can be a multiple of 5 or a multiple of 7 or a combination of both. Therefore, we form an equation like 5x + 7y where x represents the number of $5 chips and y represents the number of $7 chips. Note that both x and y may be ZERO in certain cases.
The best approach beyond this stage is to eliminate options based on whether 5x+7y can give us that particular value or not.
5x + 7y = 31 can be satisfied by taking x = 2 and y = 3. $31 can be dealt out using the chips.
5x + 7y = 29 can be satisfied by taking x = 3 and y = 2. $29 can be dealt out using the chips.
5x + 7y = 26 can be satisfied by taking x = 1 and y = 3. $26 can be dealt out using the chips.
5x + 7y = 21 can be satisfied by taking x = 0 and y = 3. $21 can be dealt out using the chips.
$23 is the only amount which cannot be expressed in terms of either a multiple of 5 or a multiple of 7 or both.
Answer options A, B, C and E can be eliminated. The correct answer option is D.
Hope that helps!
The best approach beyond this stage is to eliminate options based on whether 5x+7y can give us that particular value or not.
5x + 7y = 31 can be satisfied by taking x = 2 and y = 3. $31 can be dealt out using the chips.
5x + 7y = 29 can be satisfied by taking x = 3 and y = 2. $29 can be dealt out using the chips.
5x + 7y = 26 can be satisfied by taking x = 1 and y = 3. $26 can be dealt out using the chips.
5x + 7y = 21 can be satisfied by taking x = 0 and y = 3. $21 can be dealt out using the chips.
$23 is the only amount which cannot be expressed in terms of either a multiple of 5 or a multiple of 7 or both.
Answer options A, B, C and E can be eliminated. The correct answer option is D.
Hope that helps!
