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# If George had 16 more textbooks, he would have three times

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Intern
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If George had 16 more textbooks, he would have three times [#permalink]

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27 Dec 2012, 09:56
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If George had 16 more textbooks, he would have three times as many textbooks as Ann does. Does George have more textbooks than Ann has?

(1) Ann has more than 5 textbooks
(2) George has fewer than 8 textbooks
[Reveal] Spoiler: OA
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Re: If George had 16 more textbooks, he would have three times [#permalink]

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27 Dec 2012, 10:07
2
KUDOS
tim415 wrote:
If George had 16 more textbooks, he would have three times as many textbooks as Ann does. Does George have more textbooks than Ann has?

(1) Ann has more than 5 textbooks
(2) George has fewer than 8 textbooks

Suppose George has G books and Ann has A books then
G + 16 = 3A
is G > A?

STAT1: A > 5
G = 3A - 16 if A is 2000 then G = 6000 - 16 > 2000 (> A)
But if A = 6 then G = 2, so G < A
so, NOT SUFFICIENT

STAT2: G < 8
G + 16 = 3A => G = 3A -16 < 8
3A < 24
A < 8
For Any value of A < 8 G will be always less than A
A = 7 => G = 3*7 - 16 = 5
A = 6 => G = 3*6 - 16 = 2
A = 5 or less will give negative values of G so not possible
Hence G < A
so, SUFFICIENT.
Hope it helps!
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Re: If George had 16 more textbooks, he would have three times [#permalink]

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27 Dec 2012, 16:31
tim415 wrote:
If George had 16 more textbooks, he would have three times as many textbooks as Ann does. Does George have more textbooks than Ann has?

(1) Ann has more than 5 textbooks
(2) George has fewer than 8 textbooks

George = x, Ann = (x+16)/3

question: is x>(x+16)/3 i.e. is x>8

from 1
x+16>15,i.e. x>-1...not suff

from 2
x<8...suff

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Re: If George had 16 more textbooks, he would have three times [#permalink]

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28 Dec 2012, 08:56
But if George had 0 books, this doesn't work and the answer would be E
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Re: If George had 16 more textbooks, he would have three times [#permalink]

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20 Feb 2013, 19:33
tbhagnari wrote:
But if George had 0 books, this doesn't work and the answer would be E

Consider that George had 0 books. If he had 16 more books, the total number of books would be 16. This would be equal to 3 times the number of books Ann has. 16=3(Ann's books)

Hence, Ann's books=16/3

This is a decimal. One cannot have books in decimal and thus George cannot have 0 books.

Hope that helps.
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Re: If George had 16 more textbooks, he would have three times [#permalink]

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22 Feb 2013, 04:42
tim415 wrote:
If George had 16 more textbooks, he would have three times as many textbooks as Ann does. Does George have more textbooks than Ann has?

(1) Ann has more than 5 textbooks
(2) George has fewer than 8 textbooks

if x+16=3y,i.e. if x = 3y-16, is x>y

from 1 , y>5, using w.c.s put y = 6 (no half books are allowed) then x = 2 and y>x put y = 200 then x = 584 and x>y..insuff

from 2

x<8 , y or and x has to be whole numbers ( i.e. books) thus what ever values x takes x+16 has to be a multiple of 3 ,i.e. x+16= ( x= 2, 5) , in all cases y is always greater ........suff

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Re: If George had 16 more textbooks, he would have three times [#permalink]

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22 Feb 2013, 05:43
If George had 16 more textbooks, he would have three times as many textbooks as Ann does. Does George have more textbooks than Ann has?

(1) Ann has more than 5 textbooks
(2) George has fewer than 8 textbooks

This question can be done using algebra.

G + 16 = 3A

Statement (1):
If A = 6 then G = 2 (NO: George does not have more textbooks than Ann)
If A = 12 then G = 20 (YES: George have more textbooks than Ann)

Since we got a Yes and a No then means this statement is insufficient to give us a clear answer.

Statement (2): (Let us try to give George the maximum number of notebooks)
If G = 5 then A = 7 (NO: George does not have more textbooks than Ann)
Even after having maximum number of notebooks George has less notebooks than Anne, hence in every case George will have less notebooks than Anne. Hence the answer is (B)
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Re: If George had 16 more textbooks, he would have three times [#permalink]

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14 May 2015, 10:44
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Re: If George had 16 more textbooks, he would have three times [#permalink]

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21 Aug 2016, 07:22
tim415 wrote:
If George had 16 more textbooks, he would have three times as many textbooks as Ann does. Does George have more textbooks than Ann has?

(1) Ann has more than 5 textbooks
(2) George has fewer than 8 textbooks

I don't agree with the answer. Please clarify the mistake in my reasoning, Veritas

Assume number of Geogre's books = G
number of Ann's books = A

==> G + 16 = 3A ==> G - A = 2A - 16
G - A > 0 ONLY IF 2A - 16> 0 or A > 8
G - A < 0 ONLY IF 2A- 16 <0 or A < 8

(1) or/and (2) are not sufficient.
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Re: If George had 16 more textbooks, he would have three times   [#permalink] 21 Aug 2016, 07:22
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