BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

Is pq a multiple of 24?

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Legendary Member
Posts: 641
Joined: Tue Feb 14, 2012 3:52 pm
Thanked: 11 times
Followed by:8 members

Is pq a multiple of 24?

by gmattesttaker2 » Tue Feb 18, 2014 11:40 pm
Hello,

Can you please assist with this:

If p and q are two consecutive positive integers, is pq a multiple of 24?

(1) p is a multiple of 8.
(2) q is an odd integer.


I am getting A


My approach:

Let the 2 consecutive integers be p(p+1)

Is: p(p+1) a multiple of 24?

1) p is a multiple of 8

Hence is 8(8+1) a multiple of 24? - Yes. Hence, suff.


2) q is an odd integer

Let q = 3. Hence, p = 2 - Is pq a multiple of 24 - No.
However as seen above when p = 8 and q = 9, pq is a multiple of 24.

Hence, in-suff.


Hence, A


Thanks for your help,
Sri
Top
Source: — Data Sufficiency |

GMAT/MBA Expert

User avatar
Elite Legendary Member
Posts: 10392
Joined: Sun Jun 23, 2013 6:38 pm
Location: Palo Alto, CA
Thanked: 2867 times
Followed by:511 members
GMAT Score:800

by [email protected] » Wed Feb 19, 2014 12:18 am
Hi Sri,

We don't know if P or Q is the bigger number. With THAT idea in mind, how would you answer this question differently?

GMAT assassins aren't born, they're made,
Rich
Contact Rich at [email protected]
Image
Top

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 16207
Joined: Mon Dec 08, 2008 6:26 pm
Location: Vancouver, BC
Thanked: 5254 times
Followed by:1268 members
GMAT Score:770

by Brent@GMATPrepNow » Wed Feb 19, 2014 7:30 am
gmattesttaker2 wrote:Hello,

Can you please assist with this:

If p and q are two consecutive positive integers, is pq a multiple of 24?

(1) p is a multiple of 8.
(2) q is an odd integer.


I am getting A


My approach:

Let the 2 consecutive integers be p(p+1)

Is: p(p+1) a multiple of 24?

1) p is a multiple of 8

Hence is 8(8+1) a multiple of 24? - Yes. Hence, suff.


2) q is an odd integer

Let q = 3. Hence, p = 2 - Is pq a multiple of 24 - No.
However as seen above when p = 8 and q = 9, pq is a multiple of 24.

Hence, in-suff.


Hence, A


Thanks for your help,
Sri
Hey Sri,

The problem with your solution is highlighted above in blue.
Statement 1 says that p is a multiple of 8, but you have let p EQUAL 8
If you had also tested p = 16, you'd find that p(p+1) = (16)(17), which is not divisible by 24.

Of course, as Rich mentioned, you have also assumed that q > p, but the question does not state this.

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
Image
Top

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 16207
Joined: Mon Dec 08, 2008 6:26 pm
Location: Vancouver, BC
Thanked: 5254 times
Followed by:1268 members
GMAT Score:770

by Brent@GMATPrepNow » Wed Feb 19, 2014 7:42 am
gmattesttaker2 wrote: If p and q are two consecutive positive integers, is pq a multiple of 24?

(1) p is a multiple of 8.
(2) q is an odd integer.
Target question: Is pq a multiple of 24?

Given: p and q are two consecutive positive integers

Let's head straight to . . .

Statements 1 and 2 combined
There are several values of p and q that satisfy the conditions in both statements. Here are two:
Case a: p = 8 and q = 9 (so pq = 72), in which case pq is a multiple of 24
Case b: p = 8 and q = 7 (so pq = 56), in which case pq is NOT a multiple of 24
Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Answer = E

----------------------------------------------------
If we assume that p and q are two consecutive positive integers AND p < q, the answer is still E

Once again, we'll head straight to . . .

Statements 1 and 2 combined
There are several values of p and q that satisfy the conditions in both statements. Here are two:
Case a: p = 8 and q = 9, in which case pq is a multiple of 24
Case b: p = 16 and q = 17, in which case pq is NOT a multiple of 24
Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Answer = E


Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
Image
Top
Post new topic Post Reply
• Page 1 of 1