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Word Problems - Manhattan Gmat

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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.
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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)
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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.
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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.
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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.
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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
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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.
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by shanice » Thu Apr 19, 2012 7:16 am
Thanks, guys
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