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OG13 Q91 - Word Problems (Rates/Work)

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OG13 Q91 - Word Problems (Rates/Work)

by basso25@ » Wed Apr 10, 2013 8:14 am
if q is an odd number and the median of q consecutive integers is 120, what is the largest of these integers?

a) q-1/2 + 120
b) q/2 + 119
c) q/2 + 120
d) q+119/2
e) q+120/2

i can't understand the og13 answer explanation insufficient; therefore, please explain how you got the correct answer simply, please.
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by Anju@Gurome » Wed Apr 10, 2013 8:21 am
basso25@ wrote:if q is an odd number and the median of q consecutive integers is 120, what is the largest of these integers?

a) (q-1)/2 + 120
b) q/2 + 119
c) q/2 + 120
d) (q+119)/2
e) (q+120)/2
You haven't posted the options properly.

Easiest method to solve this problem is to plug q = 1.
Hence, there is only one integer : 120.

So the correct option should yield 120 when q = 1.

a) (q-1)/2 + 120 = 120
b) q/2 + 119 = Not integer
c) q/2 + 120 = Not integer
d) (q+119)/2 = 60
e) (q+120)/2 = Not integer

The correct answer is A.
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by Brent@GMATPrepNow » Wed Apr 10, 2013 8:34 am
basso25@ wrote:if q is an odd number and the median of q consecutive integers is 120, what is the largest of these integers?

a) (q-1)/2 + 120
b) q/2 + 119
c) q/2 + 120
d) (q+119)/2
e) (q+120)/2
Here's another approach.

If q is odd, then the median of the q integers will be the middle number.
So, of the q integers, the middle number is 120
Of the remaining q-1 integers (not counting 120), half of them are greater than 120 and half are less than 120.
In other words, (q-1)/2 of the integers are greater than 120.
Aside: (q-1)/2 represents half of the remaining q-1 integers.
So, to find the biggest number, we'll take the median (120) and add (q-1)/2 to get ...
120 + (q-1)/2
Answer = A

Cheers,
Brent
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by basso25@ » Wed Apr 10, 2013 8:42 am
anju: sorry about that, thanks for correcting.

anju/brent: thank you both for your explanations; combined, they've given me a stronger hold on this question.
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by vipulgoyal » Wed Apr 10, 2013 9:17 pm
Brent,
I have a query here
its not necessary that q-1/2 numbers are greater then median
for example 119 119 120 120 120
more over here the geatest is NOT 122
120 + (5-1)/2 = 122
please shed some light
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by Anju@Gurome » Wed Apr 10, 2013 9:22 pm
vipulgoyal wrote:Brent,
I have a query here
its not necessary that q-1/2 numbers are greater then median
for example 119 119 120 120 120
more over here the geatest is NOT 122
120 + (5-1)/2 = 122
please shed some light
Read the question again.
It said "q consecutive integers"
Your example, '119 119 120 120 120' are not 5 consecutive integers.
Anju Agarwal
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by vipulgoyal » Wed Apr 10, 2013 9:26 pm
thanks for prompt response, missing my glasses
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