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Consecutive integers

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Consecutive integers

by SaraLotfy » Thu Sep 19, 2013 12:34 am
Set A contains the consecutive integers ranging from x to y inclusive. If the number of integers in set A that are less than 75 is equal to the number of integers that are greater than 75, what is the value of 3x+3y?

A)225
B)300
C)372
D)450
E)528
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by theCodeToGMAT » Thu Sep 19, 2013 12:47 am
ANSWER [spoiler][D][/spoiler]

METHOD 1
Let the Sequence be

72, 73, 74, 75, 76, 77, 78 so that number of integers less than 75 is equal to number of integers greater than 75. In other words, 75 is MEAN

so,
3 (x + y) = 3 ( 72 + 78 ) = 450


METHOD 2
or, solving by logic

If the Series is AP then (First number + Last number)/2 = Mean
So, x + y = 150

Hence, 3 ( x + y ) = 450
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by SaraLotfy » Thu Sep 19, 2013 1:19 am
you are right.
I actually got the answer A, because I forgot to apply the equation (last + first)/ 2 = Mean
Instead I computed Last + first = Mean !!

Silly mistake
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by GMATGuruNY » Thu Sep 19, 2013 1:24 am
SaraLotfy wrote:Set A contains the consecutive integers ranging from x to y inclusive. If the number of integers in set A that are less than 75 is equal to the number of integers that are greater than 75, what is the value of 3x+3y?

A)225
B)300
C)372
D)450
E)528
Plug in the simplest possible case: x=74, 75, y=76.
3x + 3y = 3(x+y) = 3(74+76) = 450.

The correct answer is D.
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by theCodeToGMAT » Thu Sep 19, 2013 1:27 am
It happens :)..
Welcome to the community; i see you joined the site today only.
SaraLotfy wrote:you are right.
I actually got the answer A, because I forgot to apply the equation (last + first)/ 2 = Mean
Instead I computed Last + first = Mean !!

Silly mistake
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