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12 Nov 2022, 03:29
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C
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Difficulty:
35%
(medium)
Question Stats:
73% (01:41) correct
27%
(01:56)
wrong
based on 48
sessions
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The integer k is the product of four different prime numbers. If the result when k is divided by 10 is a multiple of 11, which of the following could be the result when k divided by 5?
A. 50
B. 55
C. 66
D. 121
E. 198
A. 50
B. 55
C. 66
D. 121
E. 198
12 Nov 2022, 04:20
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Bunuel
Since the result when k is divided by 10 = 2 * 5 is an integer, it follows that two of the four primes are 2 and 5. Further, since the result is a multiple of 11, the third prime number must be 11. Thus, k is of the form 2 * 5 * 11 * some prime number. When k is divided by 5, the result will be 2 * 11 * some prime number, which is a multiple of 22. Of the answer choices, only 66 and 198 are multiples of 22, however, 198 cannot be the result when k is divided by 5 because if it were, then k would be 990, which is not a product of four different prime numbers (there are two 3s in 990). The only possible answer is 66.
Answer: C
