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# What is the value of n in the above list? (1) The range of the number

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Intern
Joined: 18 Oct 2019
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What is the value of n in the above list? (1) The range of the number  [#permalink]

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Updated on: 29 Jan 2020, 10:29
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00:00

Difficulty:

35% (medium)

Question Stats:

61% (00:46) correct 39% (00:44) wrong based on 18 sessions

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8, 5, 19, n, 11, 7, 23

What is the value of n in the above list?

(1) The range of the numbers on the list is 23.
(2) n < 5

I got the answer as C, but looks like A is the correct choice. Could someone shed light on this? TIA

Originally posted by flower123 on 29 Jan 2020, 09:26.
Last edited by Bunuel on 29 Jan 2020, 10:29, edited 1 time in total.
Renamed the topic and edited the question.
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Re: What is the value of n in the above list? (1) The range of the number  [#permalink]

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29 Jan 2020, 09:50
I also agree the answer is C

A is insufficient as for e.g n can be 0 or n can be 28 to get a range of 23
B is insufficient in itself
When taken together we can say that the only value of n <0 that gives a range of 23 is 0.

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What is the value of n in the above list? (1) The range of the number  [#permalink]

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29 Jan 2020, 12:26
flower123 wrote:
8, 5, 19, n, 11, 7, 23

What is the value of n in the above list?

(1) The range of the numbers on the list is 23.
(2) n < 5

I got the answer as C, but looks like A is the correct choice. Could someone shed light on this? TIA

The answer is definitely C. Good job!

I have given a detailed explanation below for the benefit of others

Statement 1:

Since the range is 23, the difference between maximum and minimum is 23

In the given set (ignoring n), 5 is the smallest and 23 the largest

To make range 23, we can have 2 scenarios:

# Assuming 5 remains the smallest: The largest number = 5 + 23 = 28
Since 28 is not a number in the series, $$n$$ must be 28

# Assuming 23 remains the largest: The smallest number = 23 - 23 = 0
Since 0 is not a number in the series, $$n$$ must be 0

Thus, the value of $$n$$ can be 0 or 28 - not unique, hence insufficient

Statement 2: Just knowing n < 5 won't help us to determine the value of n - Insufficient

Combining: The value of $$n = 0$$ - Sufficient

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Re: What is the value of n in the above list? (1) The range of the number  [#permalink]

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29 Jan 2020, 13:19
flower123 wrote:
8, 5, 19, n, 11, 7, 23

What is the value of n in the above list?

(1) The range of the numbers on the list is 23.
(2) n < 5

I got the answer as C, but looks like A is the correct choice. Could someone shed light on this? TIA

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.
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Since we have 1 variable ($$n$$) and 0 equations, D is most likely to be the answer. So, we should consider each condition on its own first.

Condition 1)

Condition 1) tells the possible values of $$n$$ are $$0$$ and $$31$$.

Since condition 1) does not yield a unique solution, it is not sufficient.

Condition 2)

There are a lot of possibilities of integers less than $$5$$.

Since condition 2) does not yield a unique solution, it is not sufficient.

Conditions 1) & 2)

We have $$n = 0$$ or $$n = 31$$ from condition 1).
Since $$n < 5$$ from condition 2), we have $$n = 0$$.

Since both conditions together yield a unique solution, they are sufficient.

If the original condition includes “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations” etc., one more equation is required to answer the question. If each of conditions 1) and 2) provide an additional equation, there is a 59% chance that D is the answer, a 38% chance that A or B is the answer, and a 3% chance that the answer is C or E. Thus, answer D (conditions 1) and 2), when applied separately, are sufficient to answer the question) is most likely, but there may be cases where the answer is A,B,C or E.
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Re: What is the value of n in the above list? (1) The range of the number  [#permalink]

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29 Jan 2020, 19:28
Explanation:

Statement 1. As the range is 23. We know that range is difference between the largest & the smallest number in set.
So, if the smallest is 5, so n=28
if the largest is 23, then n= 0
Insufficient.

Statement 2: n<5. clearly insufficient as multiple values can be possible.

Combining 1 & 2:
n<5 with a range of 23, only possible value is 0.
Sufficient

IMO-C
Re: What is the value of n in the above list? (1) The range of the number   [#permalink] 29 Jan 2020, 19:28
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