Fractions - GMAT Quantitative Reasoning
Card 0 of 6
Of the marbles in a box, 
are blue, 
are red, and the rest are green. Also, half of the marbles are large and half are small. How many marbles are there?
-
Half of the blue marbles and half of the red marbles are large.
-
There are thirty-six large marbles that are either red or green.
Of the marbles in a box,
-
Half of the blue marbles and half of the red marbles are large.
-
There are thirty-six large marbles that are either red or green.
From the initial information, we can determine that 
of the balls are green.
The first statement alone tells you that half of the blue marbles and half of the red marbles are large, so half of the green marbles must be large as well. But this alone does not tell you how many marbles there are total.
The second statement alone tells you how many large marbles are red or green, but you do not have any way of figuring out how many small marbles or total marbles are.
But if you put the statements together, you know the following:
Half of the red marbles and half of the green marbles comprise the thirty-six large marbles:
There are 120 marbles.
The answer is that both statements together are sufficent to answer the question, but neither statement alone is sufficient.
From the initial information, we can determine that
The first statement alone tells you that half of the blue marbles and half of the red marbles are large, so half of the green marbles must be large as well. But this alone does not tell you how many marbles there are total.
The second statement alone tells you how many large marbles are red or green, but you do not have any way of figuring out how many small marbles or total marbles are.
But if you put the statements together, you know the following:
Half of the red marbles and half of the green marbles comprise the thirty-six large marbles:
There are 120 marbles.
The answer is that both statements together are sufficent to answer the question, but neither statement alone is sufficient.
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is a fraction in lowest terms. Is its decimal representation a terminating decimal or a repeating decimal?
Statement 1: 
is a power of 2.
Statement 2: 
is a multiple of 5.
Statement 1:
Statement 2:
The two statements together provide insufficient information.
and 
are two examples of fractions that satisfy both conditions; note that the first is represented in decimal form by a terminating decimal, and the second, by a repeating decimal.
The two statements together provide insufficient information.
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Is 
a fraction in lowest terms?
Statement 1: 
is a multiple of 4 greater than 8.
Statement 2: 
is an even number greater than 6.
Is
Statement 1:
Statement 2:
Both 
and 
satisfy the conditions of Statement 1; the first fraction is in lowest terms, the second is not.
Both 
and 
satisfy the conditions of Statement 2; the first fraction is in lowest terms, the second is not.
Neither statement alone is enough to answer the question. Both together, however, are enough to prove the fraction is not in lowest terms; a fraction which satisfies both statements has both its numerator and denominator divisible by 2.
Both
Both
Neither statement alone is enough to answer the question. Both together, however, are enough to prove the fraction is not in lowest terms; a fraction which satisfies both statements has both its numerator and denominator divisible by 2.
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Is 
a fraction in lowest terms?
Statement 1: 
is an odd number divisible by 5.
Statement 2: 
is an even number not divisible by 5.
Is
Statement 1:
Statement 2:
The two statements together are insufficient. 
and 
each satisfy the conditions of both statements, but the first fraction is in lowest terms and the second is not.
The two statements together are insufficient.
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Which fraction is larger than 
?
Which fraction is larger than
From the question, we know that only one of the fractions in the answer choices is larger than 
. The correct answer must therefore be the largest of the answer choices. This observation is important, because it means we can eliminate some of the answer choices without performing any calculations. For example, 
is smaller than 
, so eliminate 
from the possibilities. 
is smaller than both 
and 
, so eliminate it as well. Similarly, 
is smaller than 
, so eliminate 
too.
This leaves us with only two answer choices: 
and 
First consider 
. We can rewrite this as 
, which is clearly smaller than 
. Eliminate 
.
By process of elimination, we've thus shown that 
is the correct answer choice.
From the question, we know that only one of the fractions in the answer choices is larger than
This leaves us with only two answer choices:
First consider
By process of elimination, we've thus shown that
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is a real number. True or false: 
is an integer.
Statement 1: 
is an integer.
Statement 2: 
is an integer.
Statement 1:
Statement 2:
Statement 1 alone does not prove 
is or is not an integer.
For example, if 
, then
.
If 
, then
.
is an integer in only one scenario, but Statement 1 is true in both.
Now assume Statement 2 alone, and let 
. Then 
is an integer by Statement 2, and
Suppose 
is an integer. Then 
, the difference of integers, is itself an integer. But we know that this is equal to 
, which is not an integer, so, by contradiction, 
is not an integer.
Statement 1 alone does not prove
For example, if
If
Now assume Statement 2 alone, and let
Suppose
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