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19 Jun 2020, 05:20
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Difficulty:
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Question Stats:
95% (01:03) correct
5%
(01:43)
wrong
based on 60
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If a, b, and c are positive integers such that \(\frac{x}{2^a3^b5^c}\) is an integer, which of the following could be the value of x ?
A. 216
B. 225
C. 232
D. 240
E. 250
A. 216
B. 225
C. 232
D. 240
E. 250
yashikaaggarwal
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19 Jun 2020, 05:37
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Given : X/(2^a * 3^b * 5^c) = An integer
To find : Value of X
Solution: X is atleast multiple of 2*3*5 = 30
Among all option, only D is a said multiple of 30.
Answer should be D
ALTERNATIVELY,
Factorizing options,
A. 216 = 2*2*2*3*3*3 (5 is not a factor)
B. 225 = 5*5*3*3 (2 is not a factor)
C. 232 = 2*2*2*29 (3&5 both are not a factor)
D. 240 = 2*2*2*2*3*5 (Satisfying)
E. 250 = 5*5*5*2 (3 is not a factor)
Answer is D
Posted from my mobile device
To find : Value of X
Solution: X is atleast multiple of 2*3*5 = 30
Among all option, only D is a said multiple of 30.
Answer should be D
ALTERNATIVELY,
Factorizing options,
A. 216 = 2*2*2*3*3*3 (5 is not a factor)
B. 225 = 5*5*3*3 (2 is not a factor)
C. 232 = 2*2*2*29 (3&5 both are not a factor)
D. 240 = 2*2*2*2*3*5 (Satisfying)
E. 250 = 5*5*5*2 (3 is not a factor)
Answer is D
Posted from my mobile device
19 Jun 2020, 05:43
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you can either factor the numbers as the must be in a form of 2 (something)*3 (somthing)* 5 something
225 (not even-not factor of 2), 232 (no factor 5 ), 250 (not divisible by 3) are off since they dont have factors needed.
216 is not having 5
240 is even+ digits divisible by 3 + 0/5 divisible by 5.
checking- 240=2^4*5^1*3^1 (F) so 240 / F is the integer 1
225 (not even-not factor of 2), 232 (no factor 5 ), 250 (not divisible by 3) are off since they dont have factors needed.
216 is not having 5
240 is even+ digits divisible by 3 + 0/5 divisible by 5.
checking- 240=2^4*5^1*3^1 (F) so 240 / F is the integer 1
