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Updated on: 04 Dec 2014, 04:18
Originally posted by desaichinmay22 on 04 Dec 2014, 04:05.
Last edited by Bunuel on 04 Dec 2014, 04:18, edited 1 time in total.
Last edited by Bunuel on 04 Dec 2014, 04:18, edited 1 time in total.
Renamed the topic and edited the question.
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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:
45%
(medium)
Question Stats:
73% (02:33) correct
27%
(02:44)
wrong
based on 370
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The product of 2 positive integers is 720. If one of the numbers is increased by 10 and the other reduced by 1, the product remains unaltered. What is the value of the smaller of the two integers?
A) 6
B) 7
C) 8
D) 9
E) 10
A) 6
B) 7
C) 8
D) 9
E) 10
04 Dec 2014, 04:27
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desaichinmay22
\(ab = 720\);
\((a + 10)(b - 1) = 720\) --> \(ab +10b - a - 10 = 720\) --> \(720 + 10b - a - 10 = 720\) --> \(10b - a - 10 = 0\).
\(10b - a - 10 = 0\) --> \(10b - \frac{720}{b} - 10 = 0\) --> multiply by b: \(10b^2 - 10b - 720 = 0\) --> \(b^2 - b - 72 = 0\) --> \((b + 8)(b - 9) = 0\) --> \(b = 9\) (discard negative root since we know that a and b must be positive) --> \(a=80\) --> smaller number is 9.
Answer: D.
04 Dec 2014, 05:04
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desaichinmay22
let two numbers be x an y
thus, xy=720.------------1)
also, (x+10)(y-1)=720
from 1, we have (x+10)(y-1)=xy
xy-x+10y-10=xy
10y=10+x
or y=1+x/10
now for x=80 y becomes 9. and product becomes 720. thus value of smaller integer =9
