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750 < n < 1,500

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750 < n < 1,500 [#permalink] New post 25 May 2018, 16:06
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Question Stats:

77% (00:49) correct 22% (00:42) wrong based on 27 sessions
\(750 < n < 1,500\)

Quantity A
Quantity B
\(1,500-n\)
\(n-750\)


A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
[Reveal] Spoiler: OA

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Re: 750 < n < 1,500 [#permalink] New post 25 May 2018, 20:21
Carcass wrote:
\(750 < n < 1,500\)

Quantity A
Quantity B
1,500-n
n-750


A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.


Please confirm the solution for this
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Re: 750 < n < 1,500 [#permalink] New post 25 May 2018, 21:54
Carcass wrote:
\(750 < n < 1,500\)

Quantity A
Quantity B
1,500-n
n-750


A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
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Re: 750 < n < 1,500 [#permalink] New post 26 May 2018, 01:33
Expert's post
n is an integer in the range. However, it could be also a fraction.

That's is already enough without any calculation to assert that the answer is D

Hope this helps.

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Re: 750 < n < 1,500 [#permalink] New post 26 May 2018, 09:59
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Expert's post
Carcass wrote:
\(750 < n < 1,500\)

Quantity A
Quantity B
\(1,500-n\)
\(n-750\)


A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.


We can solve this question using matching operations

Given:
Quantity A: 1,500 - n
Quantity B: n - 750

Let's try to get the variables (n's) in one quantity

Add n to both quantities to get:
Quantity A: 1,500
Quantity B: 2n - 750

Add 750 to both quantities to get:
Quantity A: 2,250
Quantity B: 2n

Divide both quantities by 2 to get:
Quantity A: 1,125
Quantity B: n

We're told that 750 < n < 1,500
This means n COULD equal 1,125 in which case the two quantities are EQUAL
or n COULD equal 1,400 in which case Quantity B is GREATER

Answer: D


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Re: 750 < n < 1,500 [#permalink] New post 27 May 2018, 04:53
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When we see a range value, it's best to use the min and max value (based on my experience).

If 750<n<1500, then the min value of n will be 751 and the max is 1499. Plug in these values into the question.

When n=1499,
Quant A:1500-n= 1500-1499= 1
Quant B: n-750= 1499-750= much greater than 1. Quantity B > quantity A

However, when n=751,
Quant A: 1500-n= much greater than 1,
Quant B: n-750= 1. Quantity A > quantity B.

Since the sign can change, we should choose D
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Re: 750 < n < 1,500 [#permalink] New post 27 May 2018, 11:55
Given range -> 750 < n < 1500
Subtract n from the above equation. You'll get 750-n < 0 < 1500-n . Therefore, n - 750 > 0 and 1500 - n > 0 .
If n = 800 , then n - 750 = 50 and 1500 - n = 700 . Here B is greater.
If n = 1400 , then n - 750 = 650 and 1500-n - 100 , Here A is greater.
Hence we can conclude that D is the appropriate option.

Happy Learning!
Re: 750 < n < 1,500   [#permalink] 27 May 2018, 11:55
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