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02 Dec 2021, 10:00
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
66% (02:30) correct
34%
(02:14)
wrong
based on 160
sessions
History
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Not Attempted Yet
30, 40 and 'n' are such that every number is a factor of the product of the other two numbers. If 'n' is a positive integer, what is the difference between the maximum and minimum value of 'n' ?
A. 0
B. 1
C. 134
D. 1134
E. 1188
A. 0
B. 1
C. 134
D. 1134
E. 1188
02 Dec 2021, 10:17
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Minimum n is 12
Max 1200
Hence 1200-12 = 1188
Posted from my mobile device
Max 1200
Hence 1200-12 = 1188
Posted from my mobile device
02 Dec 2021, 18:00
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Rewrite the problem in a pedantic way so that it is easily understood:
30 is a factor of 40n
40 is a factor of 30n
n is a factor of 1200
1200
n’s greatest value is easy now… the greatest factor of 1200 is 1200
Now, let’s find the smallest value:
Prime factorization makes this task relatively easy.
30 = 2*3*5 40 = 2^3 * 5
30 is a factor of 40n: look at what factors are in 30 that are missing in 40. Those factors must be in n! -----> n needs a factor of 3 in it.
40 is a factor of 30n: Do the same. n needs a factor of 2^2 in it.
The smallest n is 2^2 * 3 = 12
1200 - 12 = 1188
E is the answer!
30 is a factor of 40n
40 is a factor of 30n
n is a factor of 1200
1200
n’s greatest value is easy now… the greatest factor of 1200 is 1200
Now, let’s find the smallest value:
Prime factorization makes this task relatively easy.
30 = 2*3*5 40 = 2^3 * 5
30 is a factor of 40n: look at what factors are in 30 that are missing in 40. Those factors must be in n! -----> n needs a factor of 3 in it.
40 is a factor of 30n: Do the same. n needs a factor of 2^2 in it.
The smallest n is 2^2 * 3 = 12
1200 - 12 = 1188
E is the answer!
