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

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.

So, Answer will be B
Hope it helps!

Watch the following video to learn the Basics of Inequalities


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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

B

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.

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

B

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)

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.

I don't understand why 2 can't work for the information (B) ?

2+16 = 18 books, and then Anna may have 6 books.
Is there some point i missed in the mathematical calculation , or cold anyone please clarify whe 5+16 ==> works , but 2+16>> 6 does not work?

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?

If George had 16 more textbooks, he would have three times as many textbooks as Ann does: G + 16 = 3A (A = (G + 16)/3)

Is G > A?
Is G > (G + 16)/3?
Is G > 8?

(1) Ann has more than 5 textbooks. If A = 6, then G = 2 < 8 but if A = 10, then G = 14 > 8. Not sufficient.

(2) George has fewer than 8 textbooks. Directly answers the question. Sufficient.

Answer: B.

Hope it's clear.
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Thank you. I'M so frustrated of nowadays(due to studying) so i'm making a lot of simple mistakes like this. :<

I tried testing values for statement 2 but I got stuck:

If George has less than 8, let's say 7. Then 7 + 16 = 3A, which gives us A = 23/3. Ann cannot have half of a textbook, so if we estimate this as a whole number, we get 7. I took this as then A = G, meaning both George and Ann have 7 textbooks...so I chose insufficient for statement 2 as well. Can someone tell me where I am going wrong?

Thanks!

The question translates "is G > 8". (2) says G < 8, so we have a NO answer to the question, which means that (2) is sufficient.

Next, George cannot have 7 textbooks, yes, but he could have 5, or 2 (fewer than 8).

Check complete solution here: https://gmatclub.com/forum/if-george-ha ... l#p1823500
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\(G + 16 = 3A\)
\(G = 3A - 16\)

(1) A > 5

We have no information about George; INSUFFICIENT.

(2) \(G < 8\)
\(G = 3A - 16\)
if \(G = 5\) then \(A = 7\)
Therefore George has fewer textbooks than Ann does.

SUFFICIENT.

Answer is B.
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