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14 Dec 2020, 01:15
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A
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:
57% (01:52) correct
43%
(02:01)
wrong
based on 147
sessions
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What is the value of the positive integer x?
(1) The least common multiple of x and 15 is 225.
(2) The least common multiple of x and 20 is 900.
Are You Up For the Challenge: 700 Level Questions
(1) The least common multiple of x and 15 is 225.
(2) The least common multiple of x and 20 is 900.
Are You Up For the Challenge: 700 Level Questions
14 Dec 2020, 01:41
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1. LCM of x and 15 is 225.
225 = 3 * 5 * 3 * 5
15 = 3 * 5
Since,LCM takes the highest powers of primes, the value of x should be 3*5*3*5 = 225.Sufficient.
2. LCM of x and 20 is 900.
900 = 2 * 3 * 5 * 2 * 3 * 5
20 = 2 * 2 * 5
so x could be 3*3*5*5 = 225
or 2*2*3*3*5*5 = 900
or 2*3*3*5*5 = 450
or some other combination of these factors. Insufficient.
So IMO, answer = A.
Posted from my mobile device
225 = 3 * 5 * 3 * 5
15 = 3 * 5
Since,LCM takes the highest powers of primes, the value of x should be 3*5*3*5 = 225.Sufficient.
2. LCM of x and 20 is 900.
900 = 2 * 3 * 5 * 2 * 3 * 5
20 = 2 * 2 * 5
so x could be 3*3*5*5 = 225
or 2*2*3*3*5*5 = 900
or 2*3*3*5*5 = 450
or some other combination of these factors. Insufficient.
So IMO, answer = A.
Posted from my mobile device
14 Dec 2020, 03:04
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Explanation:
Statement 1: The least common multiple of x and 15 is 225.
225 = 3^2 * 5^2
15 = 3 * 5
x must have two 5's and two 3's
x is 225
Sufficient
Statement 2: The least common multiple of x and 20 is 900.
900 = 3^2* 2^2 * 5^2
20 = 2^2 * 5
X must have two 5's, must have two 3's, can have at-most two 2's.
900, 450, 225.
Not Sufficient
IMO-A
Statement 1: The least common multiple of x and 15 is 225.
225 = 3^2 * 5^2
15 = 3 * 5
x must have two 5's and two 3's
x is 225
Sufficient
Statement 2: The least common multiple of x and 20 is 900.
900 = 3^2* 2^2 * 5^2
20 = 2^2 * 5
X must have two 5's, must have two 3's, can have at-most two 2's.
900, 450, 225.
Not Sufficient
IMO-A
