sanju09 wrote:If x is a positive integer divisible by 5, then which of the following could be the value of (x – 1) (x + 2) (x – 3) (x + 4)?
A. 54,260
B. 54,261
C. 54,262
D. 54,264
E. 54,265
Plug in increasing values for x and LOOK FOR A PATTERN.
If x=5, then (x – 1)(x + 2)(x – 3)(x + 4) =
4*7*2*
9.
If x=10, then (x – 1)(x + 2)(x – 3)(x + 4) = 9*
12*7*14.
If x=15, then (x – 1)(x + 2)(x – 3)(x + 4) = 14*17*
12*19.
If x=20, then (x – 1)(x + 2)(x – 3)(x + 4) = 19*22*17*
24.
In every case, the product is divisible by 12.
Thus, the correct answer choice must be a multiple of both 3 and 4.
For an integer to be a multiple of 4, its LAST TWO DIGITS must form a multiple of 4.
54,2
60
54,261
54,262
54,2
64
54,265
Eliminate every answer choice but A and D.
For an integer to be a multiple of 3, the SUM OF ITS DIGITS must be a multiple of 3.
A: 5+4+2+6+0 = 17.
Since 17 is not a multiple of 3, eliminate A.
The correct answer is
D.
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