The least multiple of 23, which when divided by 18, 21 and 24 leaves a remainder 7, 10 and 13 respectively:
1 3013
2 3024
3 3002
4 3036
1 3013
2 3024
3 3002
4 3036
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Source: Beat The GMAT — Problem Solving |
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Geva@EconomistGMAT
- GMAT Instructor
- Posts: 905
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Hi,
The number leaves odd remainder(7) when divided by 18. So number should be odd. Only A is odd
Hence A
Simplest way to solve such questions in test is to plug in values of all options.
If you want detailed method to solve such questions in general, here it is:
Let the number be n
n = 18p+7
n = 21q+10
n = 24r+13
As the difference is 11 in all the 3 cases, we add 11 on both sides
So, n+11 = 18(p+1) = 21(q+1) = 24(r+1)
So, (n+11) is multiple of 18,21,24
So, (n+11) is a multiple of LCM (18,21,24) = 504
So, n+11 = 504*a
So, n = (23*22 -2)a - 11 = 23(22a)-(2a+11)
For n to be divisible by 23 2a+11=23 => a=6
So, n = 504(6) - 11 = 3013.
The number leaves odd remainder(7) when divided by 18. So number should be odd. Only A is odd
Hence A
Simplest way to solve such questions in test is to plug in values of all options.
If you want detailed method to solve such questions in general, here it is:
Let the number be n
n = 18p+7
n = 21q+10
n = 24r+13
As the difference is 11 in all the 3 cases, we add 11 on both sides
So, n+11 = 18(p+1) = 21(q+1) = 24(r+1)
So, (n+11) is multiple of 18,21,24
So, (n+11) is a multiple of LCM (18,21,24) = 504
So, n+11 = 504*a
So, n = (23*22 -2)a - 11 = 23(22a)-(2a+11)
For n to be divisible by 23 2a+11=23 => a=6
So, n = 504(6) - 11 = 3013.
Cheers!
Things are not what they appear to be... nor are they otherwise
Things are not what they appear to be... nor are they otherwise
I did it by the same method u hv mentioned earlier, but the correct answer was given as 3024.
So I guess the answer is wrong. (source: online GMAT questionnaire)
anyways, thanks.
So I guess the answer is wrong. (source: online GMAT questionnaire)
anyways, thanks.
-
Geva@EconomistGMAT
- GMAT Instructor
- Posts: 905
- Thanked: 378 times
- GMAT Score:760
Having read through the batch of responses above, I repeat my question: Seriously?winniethepooh wrote:3024 is not even a multiple, buddy!
GMAT/MBA Expert
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Ian Stewart
- GMAT Instructor
- Posts: 2623
- Location: Montreal
- Thanked: 1090 times
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As Frankenstein pointed out above, if you're dividing some integer n by an even number like 18 and your remainder is odd, then n must be odd. So 3013 is the only possible answer choice. There's really no reason to do any work here.sunilrawat wrote:The least multiple of 23, which when divided by 18, 21 and 24 leaves a remainder 7, 10 and 13 respectively:
1 3013
2 3024
3 3002
4 3036
There is a lot of very bad GMAT material on the internet. This question, for example, is completely unrealistic, for many reasons - for a start, they don't even have the right number of answer choices. If you work from prep materials written by people who don't know the GMAT, you can waste a lot of time studying things that are completely irrelevant on the actual test, so choose your resources carefully.sunilrawat wrote:I did it by the same method u hv mentioned earlier, but the correct answer was given as 3024.
So I guess the answer is wrong. (source: online GMAT questionnaire)
For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com
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