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MathRevolution
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a, b, c, d, and e are positive integers satisfying the following. What Updated on: 06 Aug 2020, 15:55
Originally posted by MathRevolution on 05 Aug 2020, 03:17.
Last edited by MathRevolution on 06 Aug 2020, 15:55, edited 1 time in total.
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37% (02:46) correct 63% (02:43) wrong based on 114 sessions

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[GMAT math practice question]

\(a, b, c, d,\) and \(e\) are positive integers satisfying the following. What is the value of \(a + b + c + d + e\)?

A. \(10\)

B. \(12\)

C. \(14\)

D. \(16\)

E. \(18\)
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D

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a, b, c, d, and e are positive integers satisfying the following. What 05 Aug 2020, 03:23
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MathRevolution I think some constraint is missing in the question to determine value. Can you please check that.

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a, b, c, d, and e are positive integers satisfying the following. What 05 Aug 2020, 08:04
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MathRevolution
Could you please list out the constraints in the question.
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a, b, c, d, and e are positive integers satisfying the following. What 07 Aug 2020, 01:16
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=>

When we divide \(382\) by \(73\), we have the expression \(382 = 73·5 + 17\) or \(\frac{382}{73} = 5 + \frac{17}{73}.\)

When we divide \(73\) by \(17\), we have the expression \(73 = 17·4 + 5\) or \(\frac{73}{17} = 4 + \frac{5}{17}.\)

When we divide \(17\) by \(5\), we have the expression \(17 = 5·3 + 2\) or \(\frac{17}{5} = 3 + \frac{2}{5}.\)

When we divide \(5\) by \(2\), we have the expression \(5 = 2·2 + 1\) or \(\frac{5}{2} = 2 + \frac{1}{2}.\)

Then we have \(382 = 5 + \frac{17}{73}\)

Attachment:
8.5ps(a).png
8.5ps(a).png [ 6.09 KiB | Viewed 3950 times ]

Thus ,we have \(a = 5, b = 4, c = 3, d = 2\), and \(e = 2.\) Then \(a + b + c + d + e = 5 + 4 + 3 + 2 + 2 = 16.\)

Therefore, D is the correct answer.
Answer: D
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a, b, c, d, and e are positive integers satisfying the following. What 06 Nov 2023, 07:18
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Visualizing the pattern makes this pretty straightforward.

The right side shows a quotient A. The division on the left produces a quotient.

That first quotient is 5. That must equal A.

The remainder is 17 or 17/73.

Those 5s net out from both sides leaving 17/73 on the left and stuff divided into 1 on the right.

If you invert both sides you get the same as the original format with A eliminated and can now follow the same process, as in:

73/17=4 5/17 so B = 4.

Following this yields C=3, D=2 and E=2 and a sum of 16

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a, b, c, d, and e are positive integers satisfying the following. What 22 May 2026, 21:57
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