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Difficulty:
55%
(hard)
Question Stats:
59% (01:55) correct
41%
(02:02)
wrong
based on 59
sessions
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If \(1 < a < b < c < d\), what is the value of d?
(1) \(a + b + c + d = 170\)
(2) a, b, c, and d are all positive integers in the set of numbers that can be written in the form of \(2^n\), where n is also a positive integer.
(1) \(a + b + c + d = 170\)
(2) a, b, c, and d are all positive integers in the set of numbers that can be written in the form of \(2^n\), where n is also a positive integer.
Updated on: 14 Jun 2022, 01:34
Originally posted by GMATinsight on 03 Apr 2022, 05:24.
Last edited by GMATinsight on 14 Jun 2022, 01:34, edited 1 time in total.
Last edited by GMATinsight on 14 Jun 2022, 01:34, edited 1 time in total.
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If \(1 < a < b < c < d\), what is the value of d?
(1) \(a + b + c + d = 170\)
(2) a, b, c, and d are all positive integers in the set of numbers that can be written in the form of \(2^n\), where n is also a positive integer.
(1) \(a + b + c + d = 170\)
(2) a, b, c, and d are all positive integers in the set of numbers that can be written in the form of \(2^n\), where n is also a positive integer.
Question: d = ?
Given: \(1 < a < b < c < d\)
Statement 1: \(a + b + c + d = 170\)
there are many possible values of d hence
NOT SUFFICIENT
Statement 2: a, b, c, and d are all positive integers in the set of numbers that can be written in the form of \(2^n\), where n is also a positive integer.
This alone is not sifficient as we don't have any equation
NOT SUFFICIENT
Combining the statements
Let, \(a = 2^p\), \(b = 2^q\), \(c = 2^r\), \(d = 2^s\)
i.e. \(2^p + 2^q + 2^r + 2^s = 170\)
i.e. \(2^1 + 2^3 + 2^5 + 2^7 = 170\)
hence, \(d = 2^7 = 128\)
SUFFICIENT
Answer: Option C
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