If n is an integer and n = 2.3.5.7.11.13/77k then which of the following could be the value of k?
(A) 22
(B) 26
(C) 35
(D) 54
(E) 60
2006-12-12 03:12:44 · 11 answers · asked by Amuthan A 1 in Science & Mathematics ➔ Mathematics
Well, 77 = 7*11, so we can cancel the 7 and 11
in the numerator and denominator.
So n = 2*3*5*13/k .
Since n is an integer k must contain a subset of the prime
factors of the numerator.
So let's take the possibilities one at a time.
(A) 22. 22 is divisible by 11, but the numerator isn't. No.
(B) 26. The numerator is divisible by 2 and 13 so k could
be 26. Yes
(C) 35 35 is divisible by 7 but the numerator isn't. No.
(D) 54 54 is divisible by 9 but the numerator isn't. No.
(E) 60 60 is divisible by 4 but the numerator isn't. No.
So the only possibility is (B) 26.
2006-12-12 03:27:13 · answer #1 · answered by steiner1745 7 · 1⤊ 0⤋
Since n is an integer, the denominator 77k divides the numerator.
77 divides 7*11, so k is a divisor of 2*3*5*13.
Only choice B 26 = 2*13 is a divisor of 2*3*5*13.
2006-12-12 03:17:52 · answer #2 · answered by mulla sadra 3 · 1⤊ 0⤋
22
2006-12-12 03:23:29 · answer #3 · answered by raj 7 · 0⤊ 1⤋
It's 26....
2006-12-12 19:55:46 · answer #4 · answered by Eshwar 3 · 0⤊ 0⤋
I get 22
2006-12-12 13:03:56 · answer #5 · answered by smart-crazy 4 · 0⤊ 0⤋
77=7*11.
So this gets cancelled from noth the numerator and denominator.So, k must divide 2.3.5.13
Only (b)26 divides 2.3.5.13
2006-12-12 15:12:54 · answer #6 · answered by Anonymous · 0⤊ 0⤋
26(b)
2006-12-12 19:20:08 · answer #7 · answered by shabbarboy1991 2 · 0⤊ 0⤋
answer is 26
2006-12-12 07:00:40 · answer #8 · answered by mohanan p 1 · 0⤊ 0⤋
(B) 26
2006-12-12 16:15:05 · answer #9 · answered by arpita 5 · 0⤊ 0⤋
I have found 330
2006-12-12 03:20:01 · answer #10 · answered by maussy 7 · 0⤊ 1⤋