Is the value of n closer to 50 than to 75 ?

SOLUTION:

Is the value of n closer to 50 than to 75 ?

The point on the number line which is halfway between 50 and 75 is \(\frac{50+75}{2} = 62.5\). If \(n < 62.5\), then n is closer to 50 and if \(n > 62.5\), then n is closer to 75.

(1) 75- n>n-50 --> \(n < 62.5\) --> n is closer to 50. Sufficient.

(2) n> 60 --> n can be less as well as more than 62.5. Not sufficient.

Answer: A.
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A

1) if you simplify 75-n > n-50 we get n<62.5 ; this condition is sufficient to say that n is closer to 50 than to 75 .

2) not enough information both n=61 and n=71 yield different results .

Statement 1) 75-n > n -50 => 25 > 2n => n < 25/2 = 12.5 .
n can take any value less than 12.5 and whatever value it takes it will be closer to 50 than 75 (If you can visualize a number line).
Hence Sufficient.

Statement 2) n > 60
n can take value for example 61. Difference between 50 and 61 = 11 .Difference between 75 and 61 = 14 . So it is closer to 50.
n can also take a value of 75 which is closest to 75.
Hence Not sufficient.

Hence Option A)

Before moving on to the statements, we can find out that if n<62.5(midway between 50 and 75), the value of n will be closer to 50 than to 75. So, the question can be rephrased:

Is n<62.5?

(1). 75- n>n-50
2n<125;
n<62.5;

Since n is less than 62.5, the statement is sufficient alone.

(2) n>60;
If n is between 60 and 62.5, the answer is yes;
If n>62.5; the answer is no;

The statement is insufficient.

Ans is (A).

Answer is A.

Here is the solution

On a number line mark two point i.e. 50 and 75.Just imagine a point n which satisfy the condition that n is closer to 50 than 75 i.e we are talking about distance of n from 50 and 75.

1) 75-n> n-50. this n means n is lesser than 75 and it must be less than 67.5 i.e. midpoint of 50 and 75 to be closer to 50. Hence it is sufficient.
2)n>60 . This mean n is closer to 50 for n=60 but n is closer to 75 for n=70. Hence .It is not sufficient.
A is correct.

[quote="Bunuel"]The Official Guide For GMAT® Quantitative Review, 2ND Edition

Is the value of n closer to 50 than to 75 ?

(1) 75- n>n-50
(2) n> 60

The exact middle would be (50 + 75)/2 = 62.5.

Statement I is sufficient
-2n > -125
n < 62.5
We are sure that n is towards 50

Statement II is insufficient
n can be 61(towards 50) or 70 (towards 75)

Hence answer is A

Required: value of n closer to 50 or to 75?

Statement 1: 75-n > n -50
On simplifying, 25 > 2n or n < 25/2
n < 12.5
In this case, the difference between n and 50 will always be smaller than the difference between n and 75.
SUFFICIENT

Statement 2: n > 60
By taking values,
If n = 61.
Difference between 50 and 61 = 11
Difference between 75 and 61 = 14 . Hence n is closer to 50 for this value,

But if n = 75
Difference between 50 and 75 = 25
Difference between 75 and 75 = 0 . Hence n is closer to 75 for this value,

INSUFFICIENT

Correct Answer: Option A

Hi,

First i like to thank VeritasKarishma, for teaching weighted averages. if you master that concept ,it could be used in variety of problems. It finds applications in most of the question on GMAT. Most importantly if you can find the scenarios you can use the concept you would be saving 5 to 7 mins on the exam. Similar example is this question.

What are we asked. Does n lie closer to 50 than to 75. If i know the weights of 50 and weights of 75 i could say where would n lie. Say weight on 50 side were to be more than n would lie closer to 50 than to 75. But if weights on 75 side were more than we could conclude that n would be closer to 75 than to 50.

if you knew the allegation or weighted averages technique. This is how it would turn out . Let weights on 50 side be \(w_1\)and weights on 75 side be \(w_2\), then we know that \(\frac{ 75-n}{n-50}=\frac{w_1}{w_2}\). Can we say that \(75-n=w_1\) and \(n-50=w_2\)

Now Statement A: This statement precisely says that \(w_1>w_2\). so we can conclude that n will be closer to 50 than to 75

Statement B: n>60 Since n takes any value more than 60 we can't conclude conclusively that n will be closer to 50 than to 75

I did not do any of the calculations for this question and yes people did solve it in < 60sec. But I have learnt one point brain uses energy during the real battle. We must learn to use this energy so that for the fierce enemy we do have enough to conquer and win.

Probus
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Is the value of n closer to 50 than to 75 ?

(1) 75- n>n-50

62.5 > n

SUFFICIENT.

(2) n> 60

We can't conclude if n is closer to 50 or 75. If n is 61 then it's closer to 50. If n = 70 it's closer to 75. INSUFFICIENT.

Answer is A.
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Is the value of n closer to 50 than to 75 ?

(1) 75- n>n-50
2n < 125
n < 62.5

75 - 50 = 25
25 / 2 = 12.5
75 - 12.5 = 62.5 <--- If it's smack dab on 62.5 then we can get a no answer, but since n < 62.5, we know definitively that it's closer to 50.

Sufficient.

(2) n> 60

n = 61 then YES
n = 10000000 then NO

A.
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