If x

Question

If x<8/5, which of the following could be greater than 1?

I. 60 percent of x 
 II. 0.125 times 2x 
 III. 1/x percent of 16x

A. None
B. I only
C. II only 
D. III only
E. I and III

chetan2u · Accepted Answer

Her we have to check each option.

1. 60% of x
X<8/5 or 60% of x < 60% of 8/5 = 0.6*1.6 =0.96……cannot be greater than 1

2. 0.125 times 2x
x<8/5 or 2x<2*8/5 or 0.125*2x<0.125*2*1.6=0.25*1.6=0.4….cannot be greater than 1

3. 1/x % of 16x 
1/100x * 16x = 0.16… Again no

None possible

A

Posted from my mobile device

Kinshook · Answer

@delphsanAsked:  If x<8/5, which of the following could be greater than 1?

I. 60 percent of x
60% of x = .6x < .6*8/5 = .96 < 1: Can not be greater than 1. 
 II. 0.125 times 2x
.125*2x = .25x < .25*8/5 = .4 < 1: Can not be greater than 1. 
 III. 1/x percent of 16x
1/100x * 16x = 16/100 = .16 < 1: Can not be greater than 1.

A. None
B. I only
C. II only 
D. III only
E. I and III

IMO A

KarishmaB · Answer

We will check at x = 8/5 for ease.

I. 60 percent of x

60% is 3/5.

\frac{3}{5} * x = \frac{3}{5} * \frac{8}{5} = \frac{24}{25}

If x is less than 8/5, this will become even smaller. Hence it will never be more than 1.

II. 0.125 times 2x

.125 = \frac{1}{8}

\frac{1}{8} * 2x = \frac{1}{8} * 2 * \frac{8}{5} = \frac{2}{5}

If x is less than 8/5, this will become even smaller. Hence it will never be more than 1.

III. 1/x percent of 16x

1/x = 5/8

\frac{5/8}{100} * 16x = \frac{5}{8*100} * 16*\frac{8}{5} = \frac{16}{100}

If x is less than 8/5, this will become even smaller. Hence it will never be more than 1.

Answer (A)

Check the Percentages video here:  https://youtu.be/HxnsYI1Rws8

Bixy34 · Answer

Can someone help me understand what am I doing wrong in the 3rd statement- 1/x% of 16x? Usually whenever I am doing % of something I divide it by 100. So here is what I am doing- (1/x)/100 *16x i.e 100/x *16x. x cancels out- the answer is 1600 which is greater than 1

Bunuel · Answer

(1/x)/100 *16x =

= 1/(100x) * 16x =

= 16/100

ponderare · Answer

how can I be certain, while doing the test, that the text intends (1/x)percent, therefore 1/100x, and not 1/(x percent)=1/(x/100)=100/x? in the second case I would have chosen D.

Bunuel · Answer

“A percent of B” always means (A/100) * B.

So “1/x percent of 16x” means (1/x)% * 16x = (1/x)/100 * 16x.

If it were the way you interpreted it, it would have to been written as "1/(x percent)...".

ZeroSquare · Answer

I marked C as when I considered 7/5 I got 7/2 on solving. Please advise.

chetan2u · Answer

0.125 times 2x means o.125*2x or 0.25x
If x is 7/5, then 0.25x or x/4 = 1/4 * 7/5 or 7/20..
You may have missed a decimal point in our caculation to get 7/2 instead of 7/20

ZeroSquare · Answer

Yes, thank you! I had divided by 100 instead of 1000.

shibprasad · Answer

X < 8/5, so x could be zero...so if we do any operation on zero it will be zero and less than 1

Spamittttttttt · Answer

I took 1 as an example and solved it, is it a good approach?

chetan2u · Answer

No, that will not be correct and may give you an error in certain other options.
For example
If (i) was 80% of x instead of 60% of x.
1 will give you no. But 7/5(which is less than 8/5) will give you yes.

KarishmaB · Answer

No, the question is a lot more nuanced than that. It is a "could be greater" question. So we need to distinguish between the expressions which can never be greater than 1 and those which can be for at least some values of x.

Taking a single value of x may not help us differentiate. 
If for an expression the value turns out to be greater than 1, then fine. We know that this expression could be greater than 1. 
But if for an expression the value turns out to be less than 1, then can we say whether the expression will always be less than 1 for all possible values of x? No.

Here is a post discussing such questions:  https://anaprep.com/algebra-must-be-true-could-be-true-complete-range-questions/

If x<8/5, which of the following could be greater than 1?

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GMAT Problem Solving (PS) Questions

If x<8/5, which of the following could be greater than 1?

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