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adlakha1992
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a and b are integers. [x] is an integer less than or equal to x. 25 May 2019, 05:10
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E
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Difficulty:

95% (hard)

Question Stats:

24% (02:05) correct 76% (01:55) wrong based on 58 sessions

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a and b are integers. [x] is an integer less than or equal to x. Is [a/b]≥1?

(1) ab=64

(2) a=b^2

A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D) EACH statement ALONE is sufficient.
E) Statements (1) and (2) TOGETHER are NOT sufficient.

Can someone please help me with this question?
I have the solution as well which i could not understand. Will post that also if someone wants to check that.
Thanks in advance..

Regards,
Nandan
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E
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IanStewart
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a and b are integers. [x] is an integer less than or equal to x. 25 May 2019, 10:04
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adlakha1992
[x] is an integer less than or equal to x.
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The question doesn't really make sense, because the square brackets are not defined as what is called a 'function' in math. If I wanted to know "what is [4] equal to?", using the 'definition' in the question, "[4] is an integer less than or equal to 4". Which integer? We have no way to guess. A genuine mathematical function, on the other hand, will produce a single well-defined value any time you plug in some input value. And in any real GMAT question, if you saw something like these square brackets, it would always represent a proper function. So you will never see a question like this on the test, and it's not worth worrying about.

But if you did want a solution: using both statements, we know a = b^2, so substituting in Statement 1, b(b^2) = 64, and b^3 = 64, so b = 4 and a = 16. So the question becomes "is [16/4] less than or equal to 1?", or "is [4] less than or equal to 1?". Since the only thing we know about [4] is that it's some integer 4 or less, we have no way to know if [4] is less than 1, so the answer is E.

But I guarantee you'll never see this kind of thing on the actual test. Instead, you could see a question that begins by saying "[x] is the largest integer which is less than or equal to x" -- in that case, the square brackets represent a well-defined function, and you always know what answer it produces for any x you might plug in.
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a and b are integers. [x] is an integer less than or equal to x. 25 May 2019, 11:15
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adlakha1992
a and b are integers. [x] is an integer less than or equal to x. Is [a/b]≥1?

(1) ab=64

(2) a=b^2
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the answer would be straight E because [100] can be equal to any integer below 100 (100,99,0,-99,....)


As IanStewart already mentioned, a GMAT like question would say : [x] is the greatest integer less than or equal to x (like :https://gmatclub.com/forum/if-is-the-greatest-integer-less-than-or-equal-to-x-what-is-the-va-144277.html)
and the answer would be C in this case.
here is my 2 cents:

question: [a/b]≥1?
we are dealing with integers, so there are 4 possibilities:
a>b in magnitude, and both similar signs ---> then a/b>1 and [a/b]≥1 (yes)
a<b in magnitude, and both similar signs ---> then a/b<1 and [a/b] <1 (no)
a=b -----------------------------------------------> then a/b = 1 and [a/b]≥1 (yes)
a>b or a<b, but different signs ---------------> then a/b<0 and [a/b]<0 (no)

(1) ab=64
it means that a & b have the same sign (both negative or both positive)
(a,b) pair can be:
(64,1) or (-64,-1) --> so yes
(8,8) ------------------> so yes
(1/64) or (-1,-64) --> so no

so insufficient

(2) a=b^2
it means that a is (+ve) & b can be (+ve) or (-ve), and that a≥b (b can't be zero because it is the denominator in question stem)
(a,b) pair can be:
(1,1) ---------------------------> so yes
(4,2) or (16,4) ---------------> so yes
(1,-1) or (4,-2) or (16,-4) --> so no

so insufficient

by combining (1) and (2):
a & b must have similar signs and positive , a≥b
(a,b) pairs can be:
(8,8) -----> so yes
(16,4) ---> so yes

so sufficient
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