MGMAT prob

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taneja.niks: Senior | Next Rank: 100 Posts; Posts: 70; Joined: Tue Jun 29, 2010 9:41 am; Thanked: 2 times

by taneja.niks » Fri Apr 15, 2011 3:19 am

p and q are different two-digit prime numbers with the same digits, but in reversed order. What is the value of the larger of p and q?

(1) p + q = 110
(2) p - q = 36

what shall be he right answer??

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Source: Beat The GMAT — Data Sufficiency | Fri Apr 15, 2011 3:19 am

manpsingh87: Master | Next Rank: 500 Posts; Posts: 436; Joined: Tue Feb 08, 2011 3:07 amFollowed by: 6 members; Thanked: 72 times

by manpsingh87 » Fri Apr 15, 2011 3:33 am

taneja.niks wrote:p and q are different two-digit prime numbers with the same digits, but in reversed order. What is the value of the larger of p and q?

(1) p + q = 110
(2) p - q = 36

what shall be he right answer??

let p=10a+b;
q=10b+a;

1) p+q=110; 10a+b+10b+a=110, 11(a+b)=110; a+b=10; different numbers are possible for different values of a and b, for example (1,9),(2,8),(3,7),(4,6)..!!!
5,5 is not possible because p and q are two different numbers.
hence a alone is not sufficient to answer the question.

2)p-q=36; 10a+b-10b-a=36; 9(a-b)=36, a-b=4; different values of a and b that are possible are,(5,1),(6,2),(7,3),(8,4),(9,5)..!!! therefore 2 alone is also not sufficient to answer the question.!!!

now combine 1 and 2 we have only one common value that is (3,7)..!!
therefore answer should be C...!!!

O Excellence... my search for you is on... you can be far.. but not beyond my reach!

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HSPA: Legendary Member; Posts: 1101; Joined: Fri Jan 28, 2011 7:26 amFollowed by: 13 members; Thanked: 47 times; GMAT Score:640

by HSPA » Fri Apr 15, 2011 3:34 am

P = 10x+y and Q = 10y+x

Let us use 1: p+q = 110
11(x+y) = 110 => x+y = 10 ;
Avoid even numbers for Y.
(1,9), (3,7) , (5,5)... only 3,7 matches for P,Q sufficient

let us use 2: p-q = 36
9(x-y) = 36 => x-y = 4; Avoiding even number for y; (5,1),(7,3),(9,5)
73 is the only choice.. sufficent

Is it D?

First take: 640 (50M, 27V) - RC needs 300% improvement
Second take: coming soon..
Regards,
HSPA.

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HSPA: Legendary Member; Posts: 1101; Joined: Fri Jan 28, 2011 7:26 amFollowed by: 13 members; Thanked: 47 times; GMAT Score:640

by HSPA » Fri Apr 15, 2011 3:37 am

manap,

If it is C .. you dont need the stem support at all. just adding options will do..

C looks like a trap... what say??

First take: 640 (50M, 27V) - RC needs 300% improvement
Second take: coming soon..
Regards,
HSPA.

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taneja.niks: Senior | Next Rank: 100 Posts; Posts: 70; Joined: Tue Jun 29, 2010 9:41 am; Thanked: 2 times

by taneja.niks » Fri Apr 15, 2011 4:37 am

I agree with HSPA's solution I had the same one in mind.

@manpsingh87 u didn take the thing that the numbers need to be prime in consideration

for stat1 only 37 and 73 hold.

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force5: Legendary Member; Posts: 582; Joined: Tue Mar 08, 2011 12:48 amFollowed by: 6 members; Thanked: 61 times; GMAT Score:740

by force5 » Fri Apr 15, 2011 5:17 am

IMO D numbers should be 73 and 37

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manpsingh87: Master | Next Rank: 500 Posts; Posts: 436; Joined: Tue Feb 08, 2011 3:07 amFollowed by: 6 members; Thanked: 72 times

by manpsingh87 » Fri Apr 15, 2011 6:55 am

HSPA wrote:manap,

If it is C .. you dont need the stem support at all. just adding options will do..

C looks like a trap... what say??

agreed, i forget the initial prime number condition...!!!! answer should be D..!!!

O Excellence... my search for you is on... you can be far.. but not beyond my reach!

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Fri Apr 15, 2011 7:33 am

taneja.niks wrote:p and q are different two-digit prime numbers with the same digits, but in reversed order. What is the value of the larger of p and q?

(1) p + q = 110
(2) p - q = 36

what shall be he right answer??

It might be useful to list the possibilities before examining the statement.
Given that p and q are both 2-digit prime numbers with the the digits reversed, there are only 3 pairs of numbers to consider:

13 & 31, 17 & 71, 37 & 73

Listing possible pairs shouldn't take long because you can skip a LOT of numbers. For example, numbers beginning with 2 (21, 22, 23, etc) can be ignored because the reversed number will end with 2, which means it cannot be prime)

Statement 1
p + q = 110
This tells us that the number pair must be 37 and 73.
We don't know which number is equal to p and which number is equal to q, but it doesn't matter.
The question asks for the value of the larger number, so that answer is 73
Since we can answer the target question with certainty, statement 1 is sufficient

Statement 2
p - q = 36
Of our 3 possible pairs of numbers, only 37 & 73 meet this condition.
The larger number is 73, so statement 2 is sufficient

Answer = D

Brent Hanneson - Creator of GMATPrepNow.com

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