BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

S = {1, 2, 5, 7, x} If x is a positive integer, is the mean of set S greater than 4?

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Moderator
Posts: 7187
Joined: Thu Sep 07, 2017 4:43 pm
Followed by:23 members

S = {1, 2, 5, 7, x} If x is a positive integer, is the mean of set S greater than 4?

by BTGmoderatorDC » Sun Apr 19, 2020 6:11 pm

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

S = {1, 2, 5, 7, x}

If x is a positive integer, is the mean of set S greater than 4?

(1) The median of set S is greater than 2
(2) The median of set S is equal to the mean of set S


OA B

Source: Manhattan Prep
Top
Source: — Data Sufficiency |
Legendary Member
Posts: 2214
Joined: Fri Mar 02, 2018 2:22 pm
Followed by:5 members

Re: S = {1, 2, 5, 7, x} If x is a positive integer, is the mean of set S greater than 4?

by deloitte247 » Sat Apr 25, 2020 1:10 pm

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

$$If\ x\ >0\ is\left[\frac{summation}{number\ of\ \ S}\right]\ >\ 4$$
$$Mean\ =\ \frac{1+2+5+7+x}{5}=\frac{15+x}{5}$$
$$i.e\ \left[\frac{15+x}{3}>4\right]$$
$$15+x>20$$ $$x>5\ ??$$
The question can be rephrased as is x > 5?? because if x > 5 then (mean of S) will be > 4

Statement 1 => The median of set S is greater than 2
If x = 3 or x = 4, the median of set S will be greater than 2 but the mean of set S will be less than 4 because x is less than 5. But if x = 6, the median of set S is greater than 2 and the mean is greater than 4 because x is greater than 5 . Therefore, the exact value of x remains inconclusive, so, statement 1 is NOT SUFFICIENT

Statement 2 => The median of set S is equal to the mean of set S
$$Mean\ =\ \frac{15+x}{5}=\frac{15}{5}+\frac{x}{5}=3+\frac{x}{5}$$
Given that x is a positive integer, x has to be a multiple of 5 for it to be divisible by 5 without remainder, so if x = 5 ; then the mean = 3 + 5/5 = 4 and the median = 5, the mean and median are not equal so x cannot be 5.
If x = 10 (the next multiple of 5) then mean = 3 + 10/5 = 3 + 2 = 5 and the median = 5
x > 5 and mean > 4
Statement 2 alone is SUFFICIENT

Answer = B
Top
Post new topic Post Reply
• Page 1 of 1