Re: GMAT CLUB OLYMPICS: If x is a two-digit positive odd integer, is (x -
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26 Aug 2021, 22:51
If x is a two-digit positive odd integer, is (x - 7)(x - 5)(x - 3)(x - 1) divisible by 1920?
x is a two-digit positive odd integer, x can be from 11.... 99
(1) x + 7 is a factor of 150
150 = (5^2)(3)(2)
Total factors of 150 = 3*2*2 = 12
Factors of 150 are 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, 150
x+7 can be 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, 150
x can be 18, 23, 43, 68
Hence x can be 23, 43 (Since x is a two-digit positive odd integer)
Checking for divisibility of (x - 7)(x - 5)(x - 3)(x - 1) by 1920
Both values of x that is 23 and 43 holds when divisible by 1920 when substituted in (x - 7)(x - 5)(x - 3)(x - 1)
-Sufficient
(2) x + 17 is factor of 120
120 = (5)(3)(2^3)
Total factors of 120 = 2*2*4 = 16
Factors of 120 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120
x+17 can be 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120
x can be 13, 23, 43
Hence x can be 13, 23, 43 (Since x is a two-digit positive odd integer)
Checking for divisibility of (x - 7)(x - 5)(x - 3)(x - 1) by 1920
All values of x that is 13, 23 and 43 holds when divisible by 1920 when substituted in (x - 7)(x - 5)(x - 3)(x - 1)
-Sufficient
Answer : D