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

Redeem

PS problem

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Senior | Next Rank: 100 Posts
Posts: 76
Joined: Tue Oct 28, 2008 6:08 am
Thanked: 2 times

PS problem

by daretodream » Fri Feb 19, 2010 3:27 am
Ken withdrew $200 in cash from the bank. Using the cash, he bought a book for exactly p dollars and a hat for exactly q dollars, where p and q are two-digit integers that have the same digits but in reverse order. Assuming no sales tax, each of the following could be the amount of cash, in dollars, that Ken has remaining EXCEPT:

(A) 79
(B) 90
(C) 113
(D) 145
(E) 167
Top
Source: — Problem Solving |
User avatar
Legendary Member
Posts: 1132
Joined: Mon Jul 20, 2009 3:38 am
Location: India
Thanked: 64 times
Followed by:6 members
GMAT Score:760

by harsh.champ » Fri Feb 19, 2010 3:58 am
daretodream wrote:Ken withdrew $200 in cash from the bank. Using the cash, he bought a book for exactly p dollars and a hat for exactly q dollars, where p and q are two-digit integers that have the same digits but in reverse order. Assuming no sales tax, each of the following could be the amount of cash, in dollars, that Ken has remaining EXCEPT:

(A) 79
(B) 90
(C) 113
(D) 145
(E) 167
Let p be 10a + b (ab being the two digit no.)
Then,q=10b + a
Cash left with Ken would be $200-(11a + 11b)
=200 - 11(a+b)
Now,we are subtracting a multiple of 11 from 200.

Plugging no.s
79:- 11(a+b) =200-79 = 121
90:- 11(a+b) =200-90 = 110
113:-11(a+b) =200-113 = 87(which is not a multiple of 11)

So, the answer would be C.
It takes time and effort to explain, so if my comment helped you please press Thanks button :)



Just because something is hard doesn't mean you shouldn't try,it means you should just try harder.

"Keep Walking" - Johnny Walker :P
Top
User avatar
Legendary Member
Posts: 1275
Joined: Thu Sep 21, 2006 11:13 pm
Location: Arabian Sea
Thanked: 125 times
Followed by:2 members

by ajith » Fri Feb 19, 2010 4:03 am
daretodream wrote:Ken withdrew $200 in cash from the bank. Using the cash, he bought a book for exactly p dollars and a hat for exactly q dollars, where p and q are two-digit integers that have the same digits but in reverse order. Assuming no sales tax, each of the following could be the amount of cash, in dollars, that Ken has remaining EXCEPT:

(A) 79
(B) 90
(C) 113
(D) 145
(E) 167
p = 10a+b
q= 10b+a

p+q = 11a+11b
= 11(a+b)

Now The numbers given are 200 -( p+q)

A p+q = 121 = 11*11
B p+q = 110
C p+q = 87 Not possible

Hence C
Always borrow money from a pessimist, he doesn't expect to be paid back.
Top
Post new topic Post Reply
• Page 1 of 1