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14 Jan 2020, 05:25
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B
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Difficulty:
35%
(medium)
Question Stats:
70% (01:47) correct
30%
(02:04)
wrong
based on 92
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If the product of all the digits a 3-digit positive integer n is 160, then what is hundreds digit of n ?
(1) The units digit of n is an even number .
(2) The hundreds digit of n is an odd number .
(1) The units digit of n is an even number .
(2) The hundreds digit of n is an odd number .
14 Jan 2020, 08:28
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Bunuel
Target question: What is hundreds digit of n?
Given: The product of all the digits a 3-digit positive integer n is 160
Let's find the prime factorization of 160
160 = (2)(2)(2)(2)(2)(5)
Since each digit cannot be greater than 9, we can see that the three digits must be 4, 5 and 8.
This means that there are only six possible values of n: 458, 485, 548, 584, 845, and 854
Statement 1: The units digit of n is an even number
When we check the six possible values of n we see that four of the six possible values satisfy statement one.
Consider these two possible cases:
Case a: n = 458. In this case, the answer to the target question is the hundreds digit of n is 4
Case b: n = 548. In this case, the answer to the target question is the hundreds digit of n is 5
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: The hundreds digit of n is an odd number
Since the three digits must be 4, 5 and 8, it MUST be the case that the hundreds digit is 5
So, the answer to the target question is the hundreds digit of n is 5
Since we can answer the target question with certainty, statement 2 is SUFFICIENT
Answer: B
Cheers,
Brent
Archit3110
Major Poster
14 Jan 2020, 09:11
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for a 3 digit no ; whose product is 160
only possiblity = 8*4*5 ; which can be arranged in 6 ways
#1
The units digit of n is an even number .
8.,4 possible insufficient
#2
The hundreds digit of n is an odd number
only 5 possible
IMO b sufficient
only possiblity = 8*4*5 ; which can be arranged in 6 ways
#1
The units digit of n is an even number .
8.,4 possible insufficient
#2
The hundreds digit of n is an odd number
only 5 possible
IMO b sufficient
Bunuel
