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kiran120680
Moderator - Masters Forum
Joined: 18 Feb 2019
Last visit: 27 Jul 2022
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Location: India
Schools: AGSM '20 EDHEC Sept 2019 Intake Great Lakes '21 IE
GMAT 1: 460 Q42 V13
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17 Apr 2019, 05:06
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
5%
(low)
Question Stats:
88% (01:38) correct
12%
(02:29)
wrong
based on 137
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The product of two positive integers is 96. The sum of the two number is 22. Which of the following could be the difference of the two integers?
A. 2
B. 5
C. 6
D. 8
E. 10
A. 2
B. 5
C. 6
D. 8
E. 10
17 Apr 2019, 10:34
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\(ab = 96 = 2^5 * 3\)
\(a + b = 22\)
A few attempts will lead you to the right answer. In this case, \(96 = 16 * 6\) and \(16 + 6 = 22\). Hence, \(16 - 6 = 10\).
\(a + b = 22\)
A few attempts will lead you to the right answer. In this case, \(96 = 16 * 6\) and \(16 + 6 = 22\). Hence, \(16 - 6 = 10\).
17 Apr 2019, 17:31
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Let the two integers be x and y.
Hence from the question we know that,
xy=96
x+y=22
Or y=22-x
Hence xy = 96
can be written as
x(22-x)=96
=>22x-x(sq)=96
=>x(sq)-22x+96=0
=>x(sq)-16x-6x+96=0
=>x(x-16)-6(x-16)=0
=>(x-16)(x-6)=0
=>x=16 or x=6
Hence, y=16 or y=6 respectively
Difference between the two integers[x-y or y-x] gives us 16-6=10
Hence, option E.
Hence from the question we know that,
xy=96
x+y=22
Or y=22-x
Hence xy = 96
can be written as
x(22-x)=96
=>22x-x(sq)=96
=>x(sq)-22x+96=0
=>x(sq)-16x-6x+96=0
=>x(x-16)-6(x-16)=0
=>(x-16)(x-6)=0
=>x=16 or x=6
Hence, y=16 or y=6 respectively
Difference between the two integers[x-y or y-x] gives us 16-6=10
Hence, option E.
