Word Problems - Manhattan Gmat - The Beat The GMAT Forum - Expert GMAT Help & MBA Admissions Advice

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

Redeem

Word Problems - Manhattan Gmat

This topic has expert replies

Post new topic Post Reply

Previous Topic Next Topic

shanice: Master | Next Rank: 500 Posts; Posts: 110; Joined: Thu Apr 05, 2012 8:48 am; Thanked: 3 times; Followed by:1 members

Word Problems - Manhattan Gmat

by shanice » Wed Apr 18, 2012 12:20 am

Hi guys,

Please help me with the below problems:-

1) If Kelly received 1/3 more votes than Mike in a student election, which of the following could have
been the total number of votes cast for the two candidates?

a)12
b)13
c)14
d)15
e)16

Answer is C.

2) A store sells erasers for $0.23 and pencils for $0.11 each. If Jessica buys both erasers and
pencils from the store for a total of $1.70, what total numbers of erasers and pencils did she
buy?

Answer is 10.

I would be very grateful for sentence by sentence explanation.Thank you in advance.

Quote

Source: Beat The GMAT — Problem Solving | Wed Apr 18, 2012 12:20 am

LalaB: Master | Next Rank: 500 Posts; Posts: 425; Joined: Wed Dec 08, 2010 9:00 am; Thanked: 56 times; Followed by:7 members; GMAT Score:690

by LalaB » Wed Apr 18, 2012 1:04 am

Kelly=(4/3)*Mike

Mike+Kelly=Total

Mike +(4/3)M=Total
7/3Mike=total

since M (Mike) must be an integer, we need Total that is divisible by 7

only 14 is divisible by 7

answ choice C is right

Happy are those who dream dreams and are ready to pay the price to make them come true.(c)

In order to succeed, your desire for success should be greater than your fear of failure.(c)

Quote

aneesh.kg: Master | Next Rank: 500 Posts; Posts: 385; Joined: Mon Apr 16, 2012 8:40 am; Location: Pune, India; Thanked: 186 times; Followed by:29 members

by aneesh.kg » Wed Apr 18, 2012 1:13 am

Solution1.

Let K be the number of Kelly's votes and M be the number of Mike's votes.

K = M + 1/3*M
K = 4/3*M

Total Votes = K + M = 4/3*M + M = (7/3)*M = 7*(M/3)

which means that M is a multiple of 3 and the Total votes is a multiple of 7.

14 is the only answer that is multiple of 7, and hence (C) is the answer.

Solution2.

Let the number of erasers bought be 'e' and the number of pencils bought be 'p'
Then

0.23e + 0.11p =1.7

(Remember that bought e and p have to be integers)
Multiplying both sides of the equation by 100 so that it looks better.

23e + 11p = 170

Lets plug in a few values for 'e' starting from 1.
when we put e = 1 or 2 or 3 or 4 in the equation above, we don't get integral values for p. But when we put e = 5, we get an integral value for p which is 5.

e + p = 10

And, thats the answer.

Last edited by aneesh.kg on Wed Apr 18, 2012 2:43 am, edited 1 time in total.

Aneesh Bangia
GMAT Math Coach
[email protected]

GMATPad:
Facebook Page: https://www.facebook.com/GMATPad

Quote

GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pm; Location: New York, NY; Thanked: 13060 times; Followed by:1906 members; GMAT Score:790

by GMATGuruNY » Wed Apr 18, 2012 2:37 am

shanice wrote:Hi guys,

Please help me with the below problems:-

1) If Kelly received 1/3 more votes than Mike in a student election, which of the following could have
been the total number of votes cast for the two candidates?

a)12
b)13
c)14
d)15
e)16

To determine K:M, plug in values.
Let M=3.
Since Kelly gets 1/3 more votes, K = 3 + (1/3)3 = 4.
Thus, M:K = 3:4.
The sum of the two parts of this ratio = 3+4 = 7.
Thus, the total number of votes must be a multiple of 7.

The correct answer is C.

Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3

Quote

GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pm; Location: New York, NY; Thanked: 13060 times; Followed by:1906 members; GMAT Score:790

by GMATGuruNY » Wed Apr 18, 2012 2:40 am

A store sells erasers for $0.23 and pencils for $0.11 each. If Jessica buys both erasers and pencils from the store for a total of $1.70, what total numbers of erasers and pencils did she buy?

23e + 11p = 170.

Multiples of 23: 23, 46, 69, 92, 115, 138, 161...
Multiples of 11: 11, 22, 33, 44, 55...
Only one combination yields a sum of 170:
115+55 = 170.
Since 115 is the 5th value in the first list and 55 is the 5th value in the second list, Jessica bought 5 erasers and 5 pencils.

The correct answer is 10.

Quote

nskandan: Junior | Next Rank: 30 Posts; Posts: 15; Joined: Mon Oct 10, 2011 3:06 am; Location: UK; Thanked: 1 times

by nskandan » Wed Apr 18, 2012 6:25 am

can we use the method below

23E + 11P = 170

average cost of a E & P = (23+11)/2 = 17

17 * x = 170
x = 10 = E + P

NSK

Quote

aneesh.kg: Master | Next Rank: 500 Posts; Posts: 385; Joined: Mon Apr 16, 2012 8:40 am; Location: Pune, India; Thanked: 186 times; Followed by:29 members

by aneesh.kg » Wed Apr 18, 2012 7:17 am

23*P + 11*E = 170 is case of weighted mean.
the numbers 23 and 11 have a weight of P and E respectively.

This what you've done: 23*(x/2) + 11*(x/2) = 170
17*x = 170

,where x = E = P, and x/2 is the average. By taking an average of 23 and 11, you've assumed E = P.
So, you have already assumed something that may be wrong.

But, it came out be correct in this question and you were lucky to get the right answer.

Had the question been 23E + 11P = 159, it wouldn't have worked. You may solve and see.

Aneesh Bangia
GMAT Math Coach
[email protected]

GMATPad:
Facebook Page: https://www.facebook.com/GMATPad