tricky

[sgr21]

The smallest number which when diminished by 14, is exactly divisible 24, 32, 36, 42 and 56 is:
(A)2015
(B) 2030
(C) 2016
(D)2420

[Brent@GMATPrepNow]

The smallest number which when diminished by 14, is exactly divisible 24, 32, 36, 42 and 56 is:
(A)2015
(B) 2030
(C) 2016
(D)2420

ASIDE: A lot of integer property questions can be solved using prime factorization.
For questions involving divisibility, divisors, factors and multiples, we can say:

If N is divisible by k, then k is "hiding" within the prime factorization of N

Examples:
24 is divisible by 3 <--> 24 = (2)(2)(2)(3)
70 is divisible by 5 <--> 70 = (2)(5)(7)
330 is divisible by 6 <--> 330 = (2)(3)(5)(11)
56 is divisible by 8 <--> 56 = (2)(2)(2)(7)

Okay, now to the question.

24 = (2)(2)(2)(3)
32 = (2)(2)(2)(2)(2)
36 = (2)(2)(3)(3)
42 = (2)(3)(7)
56 = (2)(2)(2)(7)

We need a number that it is divisible by 24, 32, 36, 42 and 56

That number will = (2)(2)(2)(2)(2)(3)(3)(7) = 2016 [notice that 24, 32, 36 etc are all "hiding in this prodcut]
So, 2016 is the smallest integer that's divisible by 24, 32, 36, 42 and 56

Of course, we're subtracting 14 from some number. So, the correct answer is 2030, since 2030 - 14 = 2016

Answer: B

Cheers,
Brent

[theCodeToGMAT]

24 = 2x3x2x2
36 = 2x3x2x3
42 = 7x2x3
56 = 2x2x2x7

So, 7x2x2x2x3x3 = 504

Let multiply 504 by 4 = 2016 + 14 = 2030

Answer [spoiler]{B}[/spoiler]?

[sgr21]

thank the correct answer is 2030
bt i didnt understand how and why we did this step?

So, 7x2x2x2x3x3 = 504

please explain

[theCodeToGMAT]

thank the correct answer is 2030
bt i didnt understand how and why we did this step?

So, 7x2x2x2x3x3 = 504

please explain

For a number to be divisible by multiple divisor number, it must contain all the factors of the divisors

Lets take an example:

Suppose we need to find smallest number divisible by 2 & 5.. We need atleast 2x5 ..
If the number were 4 then it's not divisible by 5..
But if the number were 20=2x5x2.. That's dividible by 2 and 5 .. As it contains all the factors of divisor.. Although an extra 2, which doesn't impact the result

[[email protected]]

Hi sgr21,

What is the source of this question? I think this goes without saying, but this question doesn't follow proper GMAT format or style, so it's not a great example of something that you should be practicing. While some of the basic concepts behind this question will appear on the GMAT, you should still be mindful about the practice material that you're using (because if your practice material isn't realistic, then how will you know if you're ready to take the actual GMAT?).

GMAT assassins aren't born, they're made,
Rich