## Data Sufficiency Question: Multiples and Integers

## Question:

If

qis a multiple ofn, andnis a positive integer, is 360/qan integer?(1)

n< 7(2)

q< 16

## Solution:

Here we are asked to determine if 360 is evenly divisible by some number *q*. Make sure to note that, as *n* is a positive integer and *q* is a multiple of *n*, *q* must be a positive integer.

Statement 1 tells us that *n* must be less than 7. If *n* is 2, *q* can be any positive even number. Thus, *q* can be 12, in which case the answer to the question is ‘yes,’ OR *q* can be 14, in which case the answer to the question is ‘no.’ *Sometimes yes*, and *sometimes no* is insufficient in yes/no questions, therefore, statement 1 is not sufficient.

Statement 2 tells us that *q* must be less than 16. Just as was the case in statement 1, *q* can be 12, providing an answer of ‘yes,’ or *q *can be 14, providing an answer of ‘no.’ Again we have sometimes yes, sometimes no, which is NOT sufficient.

Looking at the statements together, we can immediately see that *q *could STILL equal 12 or 14 when both statements are true. Thus, together the statements are still not sufficient for the same reasons as they were insufficient alone, and your final answer **choice is E** or choice 5—there is not enough information here to answer the question.

## 13 comments

Aditya on September 2nd, 2010 at 10:18 am

Bret,

I would chose (C)...Here's the logic...

If we look at both statements together, its says that

n < 7 and q < 16

if 0 < n < 7, n = 1,2,3,4,5 or 6

Also, since q is a multiple of n and q < 16

q can be 1,2,3,4,5,6,4,6,8,9,10,12...

360/q therefore must be an integer

Hence (c)

Vivekanandan V on September 2nd, 2010 at 5:33 pm

Hi,

n = 2

q = 14

360/14 = 25.714

So C cannot be the answer!

Thanks,

Vivek.V

LeApFrOg on September 2nd, 2010 at 11:43 pm

I concur with Aditya.

Answer should be C.

anyone pls explain?

caroline on September 2nd, 2010 at 11:50 am

Sorry, but why should Q be positive? Couldn't N be multiplied by a negative number to obtain a negative Q?

Thanks..

Pasha on September 2nd, 2010 at 12:26 pm

Ofcourse the Q could be negative but whats the point !?

-14 and 14 , -12 and 12

these four numbers or better say 2 categorized numbers can lead you to E

Rohit on September 3rd, 2010 at 7:54 am

Hmmm.. why doesnt the question restrict q from being equal to zero?

Since q = 0 x n

and it is never said that q is positive...

so 360/0 wud equal infinity... is that an integer?

Does the gmat never consider such cases?

Anybody?

P.S. I agree with Aditya... ignoring the zero case (unless infinitiy is also considered an integer)... the answer should be C.. 14 can't be a multiple of a postive integer less than 7. Unless theres a typo and Bret meant less than or equal to.

Miten on September 5th, 2010 at 7:53 am

Rohit, couldn't we consider 14 as multiple of 2?

As in, 14 = 2x (x = multiple), where in this case x is 7. Therefore, q = 14, n = 2 and x = 7.

Also, since product of any number with 0 always results in 0, I doubt if could consider q = 0 x n. In this case, q could be multiple of any number not only n.

Kindly correct me wherever I am wrong as even I am learning.

Rohit on September 3rd, 2010 at 8:16 am

Bret is right....

q=14

if n=1 with a multiplier of 14....

that makes both 1 & 2 put together a yes & no...

correct ans E

but wat abt the infinity case??

LaviniaP on September 3rd, 2010 at 5:47 pm

It's E

LaviniaP on September 3rd, 2010 at 5:48 pm

My solution:

Stimulus: q/n=integer, n>0 and n= integer

Question: Is 360/q=integer? Is 2*2*2*3*3*5/q= integer?

Rephrase: Does q contain only these prime numbers?

AD

BCE

(1)n0 (stimulus) => n could be 1,2,3,4,5,6

ex: n=2 => q could be 2,4,6,8,10,12,14,16 etc.

360/12=2*2*2*3*3*5/2*2*3= integer? (YES) It’s not necessary to write all the primes (just to explain)

360/14=2*2*2*3*3*5/2*7=integer? (NO)

If we have one yes and one no answers- stop here!

360/16= 2*2*2*3*3*5/2*2*2*2= integer? (NO)- One more example

We have yes AND no answers=> not sufficient (we need a definitely yes or a definitely no answer to be correct) => eliminate A and D

BCE

(2)q q could be max.15 and cannot be 0 because DIVISION by 0 is NOT DEFINED (error). Do we care that q is positive or negative? No, because they ask for an integer (neither a positive integer nor a negative integer). For example, 360/2= 180 (integer) and 360/-2=-180 (integer)

360/15=2*2*2*3*3*5/3*5=integer? (YES)

360/14=2*2*2*3*3*5/2*7= integer? (NO)

We have yes AND no answers=> not sufficient=> eliminate B

LaviniaP on September 3rd, 2010 at 5:54 pm

My solution:

Stimulus: q/n=int, n>0 and n=integer

Question: Is 360/q=integ? Is 2*2*2*3*3*5/q=integ?

Rephrase: Does q contain only these prime numbers?

(1) 0<n n=2=> q could be 2,4,6,8,10,12,14,16, etc.

360/12=2*2*2*3*3*5/2*2*3=integ? (yes)

360/14=2*2*2*3*3*5/2*7=integ? (no)

We have a yes and a no=> not sufficient=> eliminate AD

(2)qq could be max 15

360/15=integ? (yes)

360=14=integ? (no)

we have a yes and a no=> not sufficient=> eliminate B

(1)(2) 0<n<7, q 360/15=integ(yes)

q/n=14/2=integ(yes)=> 360/14=integ(no)

we have a yes and a no=> E correct answer

LaviniaP on September 3rd, 2010 at 5:59 pm

My solution:

Stimulus: q/n=integer, n>0 and n= integer

Question: Is 360/q=integer? Is 2x2x2x3x3x5/q= integer?

Rephrase: Does q contain only these prime numbers?

AD/BCE

(1)0<n q could be 2,4,6,8,10,12,14,16 etc.

360/12=2x2x2x3x3x5/2x2x3= integer? (YES) It’s not necessary to write all the primes

360/14=2x2x2x3x3x5/2x7=integer? (NO)

If we have one yes and one no answers- stop here! Not sufficient and eliminate AD

BCE

(2)q not sufficient=> eliminate B

CE

(1)(2) 0<n<7 and q<16

q/n=15/5=integ Is 360/15=integ? (yes)

q/n=14/2=integ Is 360/14=integ? (no)

Correct answer E

LaviniaP on September 3rd, 2010 at 6:03 pm

(2)q<16, so q could be maxim 15 and cannot be 0 because division by 0 is not defined. Is it necessary to know if q is positive or negative integer? No, because the question just asks for integer. 360/15=integ? (yes) and 360/14=integ? (no)

we have yes and no answers- not sufficient-eliminate B