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Updated on: 09 Jul 2023, 01:41
Originally posted by GMATinsight on 05 Jul 2023, 04:30.
Last edited by GMATinsight on 09 Jul 2023, 01:41, edited 2 times in total.
Last edited by GMATinsight on 09 Jul 2023, 01:41, edited 2 times in total.
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Difficulty:
95%
(hard)
Question Stats:
22% (02:11) correct
78%
(01:57)
wrong
based on 37
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If x is a positive integer, find the value of x?
1) sum of x consecutive integers is x+1
2) Product of x consecutive integers is x
Source: http://www.GMATinsight.com
1) sum of x consecutive integers is x+1
2) Product of x consecutive integers is x
Source: http://www.GMATinsight.com
05 Jul 2023, 08:16
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GMATinsight
Statement 1
1) sum of x consecutive integers is x
The smallest number in the set = a
\(a + a+1 + a+2 + ... a + (x-1) = x\)
\(ax +\frac{ x(x-1)}{2} = x\)
\(\frac{2ax + x(x-1)}{2} = x\)
As x is positive, we can divide both sides by x
\(\frac{2a + (x-1)}{2} = 1\)
\(2a + x - 1 = 2\)
\(2a + x = 3\)
As a and x are positive numbers, the equation holds true x = 2 and a = 1
We have a definite value of x. Hence, the statement alone is sufficient.
Statement 2
2) Product of x consecutive integers is x
As x represents the number of consecutive integers, x the minimum value of x should be two.
\(a * (a+1) * (a+2) .. * (a + x-1) = x\)
The only value of x that's possible is 2 and the product is
\(1 * 2 = 2\)
IMO D
06 Jul 2023, 12:25
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