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25 Nov 2016, 15:44
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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:
85%
(hard)
Question Stats:
42% (01:47) correct
58%
(02:09)
wrong
based on 214
sessions
History
Date
Time
Result
Not Attempted Yet
If the LCM of x and 90 is 180,how many values can the positive integer x assume?
A)two
B)three
C)four
D)five
E)six
A)two
B)three
C)four
D)five
E)six
02 Dec 2016, 06:44
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Bookmarks
stonecold
We are given that the LCM of x and 90 is 180. We need to determine how many values can represent variable x.
We may recall that to determine the LCM of two numbers, we multiply all the prime factors with the larger exponent of the given numbers that make up the LCM. Let’s start by prime factorizing 90 and 180.
90 = 10 x 9 = 2 x 5 x 3 x 3 = 2^1 x 5^1 x 3^2
180 = 2 x 90 = 2 x 10 x 9 = 2 x 2 x 5 x 3 x 3 = 2^2 x 5^1 x 3^2
Since 90 already accounts for 5^1 and 3^2, x MUST CONTAIN 2^2. So the possible values for x are:
1) 2^2
2) 2^2 x 3^1
3) 2^2 x 3^2
4) 2^2 x 5^1
5) 2^2 x 3^1 x 5^1
6) 2^2 x 3^2 x 5^1
Answer: E
General Discussion
25 Nov 2016, 18:22
Kudos
Bookmarks
Factors of 90: 2 * 3^2 * 5
Factors of 180: 2^2 * 3^2 * 5
Thus X must contribute 2^2 while other factors can be at least of the same power as in 90.
So there are 5 possible combinations:
1] 2^2 * 3
2] 2^2 * 5
3] 2^2 * 3 * 5
4] 2^2 * 3^2 * 5
5] 2^2
Factors of 180: 2^2 * 3^2 * 5
Thus X must contribute 2^2 while other factors can be at least of the same power as in 90.
So there are 5 possible combinations:
1] 2^2 * 3
2] 2^2 * 5
3] 2^2 * 3 * 5
4] 2^2 * 3^2 * 5
5] 2^2
