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# For which of the following expressions would the value be greater if 1

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Math Expert
Joined: 02 Sep 2009
Posts: 53063
For which of the following expressions would the value be greater if 1  [#permalink]

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15 Jan 2019, 00:21
00:00

Difficulty:

55% (hard)

Question Stats:

57% (01:40) correct 43% (01:48) wrong based on 36 sessions

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For which of the following expressions would the value be greater if 160 were replaced by 120 ?

I. $$1000 - 160$$

II. $$\frac{160}{1+160}$$

III. $$\frac{1}{1-\frac{1}{160}}$$

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

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Intern
Joined: 19 Jul 2018
Posts: 10
Re: For which of the following expressions would the value be greater if 1  [#permalink]

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15 Jan 2019, 00:50
The ans to this will have to E,
Best way to check is by using small numbers, i took 2& 3,
Cheers, I really want some Kudos, so if this helped you can you please give me kudos
e-GMAT Representative
Joined: 04 Jan 2015
Posts: 2593
Re: For which of the following expressions would the value be greater if 1  [#permalink]

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15 Jan 2019, 05:41

Solution

Given:
• Three expressions

To find:
• Which among them is greater when 160 is replaced by 120 in all of them

Approach and Working:
I. 1000 – 160 = 840, and 1000 – 120 = 880.
• Thus, 880 > 840

II. 160/1+160 = 160/161, and 120/1+120 = 120/121
• Thus, 120/121 < 160/161

III. 1/1-1/160 = 160/159, and 1/1-1/120 = 120/119
• Thus, 120/119 > 160/159

Hence, the correct answer is Option E

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Re: For which of the following expressions would the value be greater if 1  [#permalink]

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21 Jan 2019, 17:51
Bunuel wrote:
For which of the following expressions would the value be greater if 160 were replaced by 120 ?

I. $$1000 - 160$$

II. $$\frac{160}{1+160}$$

III. $$\frac{1}{1-\frac{1}{160}}$$

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

Let’s examine each Roman numeral.

I. We see that 1000 - 120 is greater than 1000 - 160.

II. Originally we had 160/161, and after replacement we have 120/121, so we see the expression is smaller after the replacement.

III. When we replace 160 with 120, we see that the denominator 1 - 1/160 becomes 1 - 1/120 and thus it gets smaller. Since the numerator stays the same, the entire expression gets larger.

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Re: For which of the following expressions would the value be greater if 1   [#permalink] 21 Jan 2019, 17:51
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