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How many positive three-digit integers are divisible by both [#permalink]
16 May 2012, 11:04
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Difficulty:
15% (low)
Question Stats:
83% (02:15) correct
17% (01:35) wrong based on 205 sessions
How many positive three-digit integers are divisible by both 3 and 4?
A. 75 B. 128 C. 150 D. 225 E. 300
I know how to solve this one... but it takes me ages to find what would be the largest three digit number divisible by 12. Any tips or trick on how I can quickly get to that number?
Re: How many positive three-digit integers are divisible by both [#permalink]
16 May 2012, 11:18
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alexpavlos wrote:
How many positive three-digit integers are divisible by both 3 and 4?
A. 75 B. 128 C. 150 D. 225 E. 300
I know how to solve this one... but it takes me ages to find what would be the largest three digit number divisible by 12. Any tips or trick on how I can quickly get to that number?
Thanks!
A number to be divisible by both 3 and 4 should be divisible by the least common multiple of 3 and 4 so by 12.
How to find the largest three-digit multiple of 12: 1,000 is divisible by 4, so is 1,000-4=996, which is also divisible by 3, so 996 is the largest three-digit integer divisible by 12.
Re: How many positive three-digit integers are divisible by both [#permalink]
26 Jun 2012, 09:09
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cant say that my method is good, but still...
first, look at answer choices. u can see that these choices range widely. now divide 999 by 12 and get 83. so, u need an answer choice that is at most 83.
only 75 is less than 83. so, A is the answer. _________________
Happy are those who dream dreams and are ready to pay the price to make them come true
I am still on all gmat forums. msg me if you want to ask me smth
Re: How many positive three-digit integers are divisible by both [#permalink]
01 Oct 2012, 05:31
Multiplying 3 by 4 we get the smallest no. that is divisible by both 3 as well as 4 ... Therefore any number that is divisible by 12 is also divisible by 3 and 4 ...
Our numbers are to begin from 100 and end at 999 ...
The first three digit no. that is divisible by 12 is 108 , and the last three digit no. is 996
Now we can set up an A.P. using 108 as our first number, 996 as our last number D= 12 ..
so we get 108 , 120 , 132 .........996 ...
The nth term is 996 and to calculate the value of n we use the following formula :
Tn = a + (n-1)d
Therefore 996 = 108 + (n-1) 12
996 - 108 = (n-1) 12
888/12 = n-1
74 = n-1
n = 75 .. ( A ) _________________
"When you want to succeed as bad as you want to breathe, then you’ll be successful.” - Eric Thomas
Re: How many positive three-digit integers are divisible by both [#permalink]
01 Oct 2012, 08:32
LalaB wrote:
cant say that my method is good, but still...
first, look at answer choices. u can see that these choices range widely. now divide 999 by 12 and get 83. so, u need an answer choice that is at most 83.
only 75 is less than 83. so, A is the answer.
It is good, because with the given list of choices, it works. With another choice below 83, it would have been another story. _________________
PhD in Applied Mathematics Love GMAT Quant questions and running.
Re: How many positive three-digit integers are divisible by both [#permalink]
15 Dec 2014, 14:24
Hi Bunuel i have one question. so we need to check manually and find out the least and greatest numbers that is divisible by 3 and 4? like in this case 108 is the least number. so we have to test for each number from 100-108 is divisible by 3 and 4 or not? is this the only method?
thanks-
Bunuel wrote:
alexpavlos wrote:
How many positive three-digit integers are divisible by both 3 and 4?
A. 75 B. 128 C. 150 D. 225 E. 300
I know how to solve this one... but it takes me ages to find what would be the largest three digit number divisible by 12. Any tips or trick on how I can quickly get to that number?
Thanks!
A number to be divisible by both 3 and 4 should be divisible by the least common multiple of 3 and 4 so by 12.
How to find the largest three-digit multiple of 12: 1,000 is divisible by 4, so is 1,000-4=996, which is also divisible by 3, so 996 is the largest three-digit integer divisible by 12.
Hope it helps.
_________________
--------------------------------------------------------------------------------------------- Kindly press +1 Kudos if my post helped you in any way
Re: How many positive three-digit integers are divisible by both [#permalink]
24 Jan 2016, 16:31
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