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29 Oct 2020, 11:07
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If x is a positive integer greater than 1, and y is the smallest positive integer that is evenly divisible by every integer between 1 and x, inclusive, what is the value of x ?
(1) y = 10x
(2) y = 60
(1) y = 10x
(2) y = 60
29 Oct 2020, 22:32
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Sajjad1994
Now, had the number y been product of all numbers from 1 to x, y would have been x!. But we are looking at LCM(1 to x) = y.
(1) y = 10x
\(y=10x=1*2*5*x\), so x has to be greater than 5, and should be a multiple of 3 and 4 for sure.
we can test x for the least value after 5, that is 6..
y=10*6=60. CHECK if 60 is divisible by all numbers from 1 to 6 => Answer is YES.
so x=6
(2) y = 60
y is divisible by consecutive numbers 1, 2, 3, 4, 5, 6
Thus x can take any value - 5 or 6.
When x =5, the LCM of (1,2,3,4,5)=60
When x=6, the LCM of (1,2,3,4,5,6)=60
A
14 Nov 2020, 20:53
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chetan2u
From the first statement, we get y=60 & second statement says y=60. If y is 60 and is the smallest no. divisible between 1 and X, so X has to be six.
How can X take any value from 1 to 2,3,4,5,6? Y is supposed to be the smallest no. so if X is 3 y=2 & if X is 4 Y=6.
Shouldn't the answer be D i.e. from both the statement we can get the value of X?
