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Number of hours in n days?

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Number of hours in n days?

by gmattesttaker2 » Sat Feb 22, 2014 5:16 pm
Hello,

Can you please tell me how to solve this:

Each of the following numbers has two digits x'ed out. Which of the numbers could be the number of hours in n days, where n is an integer?

(A) 25x,x06
(B) 50x,x26
(c) 56x,x02
(D) 62x,x50
(E) 65x,x20

OA: E



Thanks a lot,
Sri
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by Brent@GMATPrepNow » Sat Feb 22, 2014 5:28 pm
gmattesttaker2 wrote: Each of the following numbers has two digits x'ed out. Which of the numbers could be the number of hours in n days, where n is an integer?

(A) 25x,x06
(B) 50x,x26
(c) 56x,x02
(D) 62x,x50
(E) 65x,x20

OA: E
This is a divisibility question in disguise.
There are 24 hours in 1 day.
Since 24 is divisible by 4, the number of hours in n days must be divisible by 4.
For example, there are 48 hours in 2 days, 72 hours in 3 days, 96 hours in 4 days, 120 hours in 5 days, 144 hours in 6 days, 168 hours in 7 days, etc.
Notice that 48, 72, 96, 120, 144, and 168 are all divisible by 4.

IMPORTANT: To determine whether an integer is divisible by 4, we need only check the number formed by the last 2 digits. If that 2-digit number is divisible by 4, the entire integer is divisible by 4.
For example, we know that 12543128 is divisible by 4 because 28 is divisible by 4.
Likewise, we know that 32873117 is NOT divisible by 4 because 17 is NOT divisible by 4.

When we check the last 2 digits of the answer choices, we see that only E is such that the number created by the last 2 digits (20) is divisible by 4. So, E is the only value that could be divisible by 4.

Cheers,
Brent
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by gmattesttaker2 » Sat Feb 22, 2014 7:00 pm
Brent@GMATPrepNow wrote:
gmattesttaker2 wrote: Each of the following numbers has two digits x'ed out. Which of the numbers could be the number of hours in n days, where n is an integer?

(A) 25x,x06
(B) 50x,x26
(c) 56x,x02
(D) 62x,x50
(E) 65x,x20

OA: E
This is a divisibility question in disguise.
There are 24 hours in 1 day.
Since 24 is divisible by 4, the number of hours in n days must be divisible by 4.
For example, there are 48 hours in 2 days, 72 hours in 3 days, 96 hours in 4 days, 120 hours in 5 days, 144 hours in 6 days, 168 hours in 7 days, etc.
Notice that 48, 72, 96, 120, 144, and 168 are all divisible by 4.

IMPORTANT: To determine whether an integer is divisible by 4, we need only check the number formed by the last 2 digits. If that 2-digit number is divisible by 4, the entire integer is divisible by 4.
For example, we know that 12543128 is divisible by 4 because 28 is divisible by 4.
Likewise, we know that 32873117 is NOT divisible by 4 because 17 is NOT divisible by 4.

When we check the last 2 digits of the answer choices, we see that only E is such that the number created by the last 2 digits (20) is divisible by 4. So, E is the only value that could be divisible by 4.

Cheers,
Brent

Hello Brent,

Thank you very much for the detailed and excellent explanation. I was just wondering how we are determining that the number of hours should be divisible by 4 and say not by 3 or 2? Thanks again for all for your help.

Best Regards,
Sri
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by Patrick_GMATFix » Sat Feb 22, 2014 9:18 pm
how we are determining that the number of hours should be divisible by 4 and say not by 3 or 2?
Sri one does not exclude the other. The # of hours is a multiple of 24, so it must be divisible by 24 and all of the factors of 24. The number of hours must be divisible by 2, 3, as well as 4 (and all other factors of 24)
  • Checking divisibility by 2 would not help us eliminate any answer choice (all choices are even)
  • Checking divisibility by 3 cannot be done (n is divisible by 3 if the sum of its digits is a multiple of 3, but we don't know all the digits)
  • Checking divisibility by 4 is not only possible (b/c the check only uses the last two digits), but also really helpful (b/c only one choice passes that check as Brent showed).
-Patrick
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