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Increase?

by oquiella » Sun Sep 27, 2015 6:52 pm
As x increases from 165 to 166, which of the following must increase?

I. 2x-5
II. 1- 1/X
III. 1/x^2-x


A. I only
B. III only
C. I and II
D. I and III
E. II and III

Please explain a quick process to solve within given time
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by GMATGuruNY » Sun Sep 27, 2015 7:45 pm
The given values are IRRELEVANT.
To make the math easier, rephrase the problem as follows:
oquiella wrote:As x increases from 2 to 3, which of the following must increase?

I. 2x-5
II. 1- 1/X
III. 1/x^2-x

A. I only
B. III only
C. I and II
D. I and III
E. II and III
I. 2x-5
If x=2, then 2x-5 = 2*2 - 5 = -1.
If x=3, then 2x-5 = 2*3 - 5 = 1.
The value of 2x-5 increases.
Eliminate any answer choice that does not include I.
Eliminate B and E.

II. 1 - (1/x)
If x=2, then 1 - 1/2 = 1/2.
If x=3, then 1 - 1/3 = 2/3.
The value of 1 - (1/x) increases.
Eliminate any answer choice that does not include II.
Eliminate A and D.

The correct answer is C.
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by [email protected] » Sun Sep 27, 2015 9:44 pm
Hi oquiella,

Roman Numeral questions are relatively rare on Test Day (you'll likely see just 1 in the Quant section), but they are almost always designed around Number Properties and logic 'shortcuts'...

Here, we're told that X increase from 165 to 166. We're asked which of the following MUST increase. While this prompt might appear 'calculation heavy', you can actually solve it WITHOUT doing calculations (but you have to pay attention to the answer choices).

I. 2X - 5

The "-5" has the same 'math effect', regardless of what X is: the '-5' reduces the value by 5. So as X goes from 165 to 166, 2X gets BIGGER. Since the '-5' has the same effect, 2X-5 definitely gets bigger as X increases from 165 to 166.
Roman Numeral 1 INCREASES
Eliminate Answers B and E.

II. 1 - 1/X

As the denominator of a fraction gets BIGGER, the fraction gets SMALLER. Thus, 1/165 > 1/166. The "1" in this calculation is constant, so subtracting a SMALLER fraction from it will lead to a BIGGER result. As X increases from 165 to 166, 1/X gets SMALLER, so 1-(1/X) definitely gets bigger.
Roman Numeral 2 INCREASES
Eliminate Answers A and D.

There's only one answer remaining (and we don't even have to deal with Roman Numeral 3)...

Final Answer: C

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by Jeff@TargetTestPrep » Sat Jul 14, 2018 6:38 pm
oquiella wrote:As x increases from 165 to 166, which of the following must increase?

I. 2x-5
II. 1- 1/X
III. 1/x^2-x


A. I only
B. III only
C. I and II
D. I and III
E. II and III
We see that we need to determine what happens when we increase a positive integer by a value of 1. We don't need to use inconvenient numbers 165 and 166. To make the calculations easier, we will use the smaller numbers 2 and 3. We can now rephrase the question as:

As x increases from 2 to 3, which of the following must increase?

Let's test out the new numbers for each Roman numeral.

I. 2x - 5

When x = 2:

2(2) - 5 = -1

When x = 3:

2(3) - 5 = 1

This DOES increase. Roman numeral I is correct.

II. 1 - 1/x

When x = 2:

1 - 1/2 = 1/2

When x = 3:

1 - 1/3 = 2/3

This DOES increase. Roman numeral II is also correct.

Since the only answer choice where both I and II are correct is C, we already know the answer at this point. However, let's also test Roman numeral III for practice.

III. 1/(x^2 - x)

When x = 2:

1/(2^2 - 2)

1/(4 - 2) = 1/2

When x = 3:

1/(3^2 - 3)

1/(9 - 3) = 1/6

This DOES NOT increase. Roman numeral III is not correct.

Thus, only I and II are correct.

Answer: C

Jeffrey Miller
Head of GMAT Instruction
[email protected]

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