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# A man sold only red and blue balloons on only small and large sizes.

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Math Expert
Joined: 02 Sep 2009
Posts: 58401
A man sold only red and blue balloons on only small and large sizes.  [#permalink]

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14 Mar 2018, 01:37
00:00

Difficulty:

25% (medium)

Question Stats:

79% (01:08) correct 21% (01:43) wrong based on 32 sessions

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A man sold only red and blue balloons on only small and large sizes. If he sold a total of 108 balloons, how many were small red balloons?

(1) He sold 35 large balloons
(2) He sold 25 small blue balloons

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Joined: 22 Feb 2018
Posts: 420
Re: A man sold only red and blue balloons on only small and large sizes.  [#permalink]

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14 Mar 2018, 01:52
Bunuel wrote:
A man sold only red and blue balloons on only small and large sizes. If he sold a total of 108 balloons, how many were small red balloons?

(1) He sold 35 large balloons
(2) He sold 25 small blue balloons

Given small red+ small blue +large red+ large blue = 108
we have to find out number of small red.

Statement 1: 35 large balloon sold
large red + large blue = 35
Small red + small blue + 35 = 108
Small red + small blue = 73.
There are 2 variable and one equation so statement 1 is not sufficient.
Statement 2 : small blue = 25
As we have to find the number of small red balloon, this statement does not give information about small red balloon's number.
So it is insufficient

Combining Statement 1 and 2 , i.e Small red + small blue = 73;small blue = 25 , we can find out the number of small red balloon.
small red+ 25 = 73
small red = 48

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Re: A man sold only red and blue balloons on only small and large sizes.  [#permalink]

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14 Mar 2018, 02:14
1
Bunuel wrote:
A man sold only red and blue balloons on only small and large sizes. If he sold a total of 108 balloons, how many were small red balloons?

(1) He sold 35 large balloons
(2) He sold 25 small blue balloons

IMO C.

This is a 2x2 matrix problem and I solve it using the famous table method.

Since we know the sum of all balloons we can fill out the details and find the required subset.

Refer to attached image. R = Red, B = Blue, S = Small and L = large.

Kudos ! if you liked the explanation...
Attachments

IMG_20180314_143722.jpg [ 720.85 KiB | Viewed 355 times ]

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Re: A man sold only red and blue balloons on only small and large sizes.   [#permalink] 14 Mar 2018, 02:14
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