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# A man purchased some pens, pencils and erasers. Can the number of eras

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Math Expert
Joined: 02 Sep 2009
Posts: 41886

Kudos [?]: 128752 [0], given: 12182

A man purchased some pens, pencils and erasers. Can the number of eras [#permalink]

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05 Jul 2017, 00:33
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Difficulty:

65% (hard)

Question Stats:

60% (01:54) correct 40% (01:33) wrong based on 52 sessions

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A man purchased some pens, pencils and erasers. Can the number of erasers purchased be 3?

(1) The ratio of the number of pens to the number of pencils was the same as the ratio of the number of pencils to the number of erasers.
(2) Total number of items purchased was 21.
[Reveal] Spoiler: OA

_________________

Kudos [?]: 128752 [0], given: 12182

Director
Joined: 18 Aug 2016
Posts: 511

Kudos [?]: 139 [0], given: 123

GMAT 1: 630 Q47 V29
A man purchased some pens, pencils and erasers. Can the number of eras [#permalink]

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05 Jul 2017, 00:46
Bunuel wrote:
A man purchased some pens, pencils and erasers. Can the number of erasers purchased be 3?

(1) The ratio of the number of pens to the number of pencils was the same as the ratio of the number of pencils to the number of erasers.
(2) Total number of items purchased was 21.

(1) gives us

Pen : Pencil : Eraser
if the ratio is

3:3:3 then we can say Yes

but if the ratio is
1:3:9 then its No
Not sufficient

(2) Total is 21

Now
Pen : Pencil : Eraser
x:y:z
x+y+z = 21
Not sufficient

On combining
x/y=y/z
y^2 = xz

Lets take one example
y = 6 and x = 12 and y = 3
Pen : Pencil : Eraser
12:6:3 answer would be Yes

"Can the number of erasers purchased be 3" Yes possible

Hence C
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We must try to achieve the best within us

Thanks
Luckisnoexcuse

Last edited by Luckisnoexcuse on 27 Sep 2017, 21:21, edited 1 time in total.

Kudos [?]: 139 [0], given: 123

Intern
Joined: 01 Jun 2016
Posts: 25

Kudos [?]: 9 [0], given: 44

A man purchased some pens, pencils and erasers. Can the number of eras [#permalink]

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27 Sep 2017, 21:02
Bunuel wrote:
A man purchased some pens, pencils and erasers. Can the number of erasers purchased be 3?

(1) The ratio of the number of pens to the number of pencils was the same as the ratio of the number of pencils to the number of erasers.
(2) Total number of items purchased was 21.

Answer C

Solution:

Let the number of pen be X,
the number of pencil be Y,
the number of Erasers be Z.

Statement 1 - \frac{X}{Y} = \frac{Y}{Z}
=> XZ = $$Y^2$$ -------------------------------------------------Equation I

Y can be any number.

Statement 1 Not sufficient

Statement 2 - X + Y + Z = 21 -------------------------------------------------Equation II

Y can be any number.

Statement 2 Not sufficient

Together 1 & 2:

From equation 1
$$Y^2$$ = Can only be equal to 4,9,16, and 25.
so, Y can be 2, 3, 4, 5.

Only when X = 16, Z = 1 and Y = 4 will satisfy both of the above equations.

hence Y = 4 and not 3 so

Together both the statements are sufficient. C

Kudos [?]: 9 [0], given: 44

Intern
Joined: 26 Feb 2017
Posts: 2

Kudos [?]: 0 [0], given: 16

Re: A man purchased some pens, pencils and erasers. Can the number of eras [#permalink]

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17 Oct 2017, 05:17
Can someone please give another simple technique to solve this?

Kudos [?]: 0 [0], given: 16

Re: A man purchased some pens, pencils and erasers. Can the number of eras   [#permalink] 17 Oct 2017, 05:17
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# A man purchased some pens, pencils and erasers. Can the number of eras

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