GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 29 May 2020, 00:14 ### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # In a certain class of 5 students, the average (arithmetic mean) weight

Author Message
TAGS:

### Hide Tags

Math Expert V
Joined: 02 Sep 2009
Posts: 64222
In a certain class of 5 students, the average (arithmetic mean) weight  [#permalink]

### Show Tags 00:00

Difficulty:   55% (hard)

Question Stats: 58% (01:45) correct 42% (02:10) wrong based on 173 sessions

### HideShow timer Statistics

GMAT Club's Fresh Challenge Problem.

In a certain class of 5 students, the average (arithmetic mean) weight of any two students in the group is less than 70 kg. How many students in the class weigh 70 kg or more?

(1) One of the students weighs more than 70 kg.
(2) The median weight of all 5 students is 68 kg.

_________________
Intern  B
Joined: 03 Jun 2015
Posts: 21
GMAT 1: 710 Q49 V44
GPA: 3.58
WE: Information Technology (Computer Software)
Re: In a certain class of 5 students, the average (arithmetic mean) weight  [#permalink]

### Show Tags

Bunuel wrote:

GMAT Club's Fresh Challenge Problem.

In a certain class of 5 students, the average (arithmetic mean) weight of any two students in the group is less than 70 kg. How many students in the class weigh 70 kg or more?

(1) One of the students weighs more than 70 kg.
(2) The median weight of all 5 students is 68 kg.

Answer should be E as none of the statements even if combined together is sufficient to answer the question.
[Given] : 5 students, average weight of any 2 students is less than 70 kg.
[Required] : Weight of all students

1. One of the students weight exceeds 70 kg. But we do not know if only one student exceeds 70 kg weight . Hence weight of other students cannot be derived . The only inference is, one student weights 70+ kg so one other student must weight less than 70 kg.
2. The median weight of all 5 students is 68 kg. So maybe all students weight 68 kg or maybe the sequence is 66, 67, 68, 69 ,70 or maybe the sequence is 66.5 67, 68, 69, 70.5 or maybe the sequence is 66 66 68 70 70 or maybe 65 65 68 71 71 .. many sequences are possible. So we do not get any definite answe.

Even if we combine the two statements, we do not achieve any concrete conclusion on how many students exceed 70 kg weight.

Hence, option E should be correct.
Please correct me if I am wrong _________________
A dream doesn't become reality through magic; it takes sweat, determination and hard work.
Senior Manager  D
Joined: 07 Dec 2017
Posts: 333
GMAT 1: 650 Q50 V28
GMAT 2: 720 Q49 V40 Re: In a certain class of 5 students, the average (arithmetic mean) weight  [#permalink]

### Show Tags

Correct mei id im woring

Sent from my ONEPLUS A3003 using GMAT Club Forum mobile app
Intern  Joined: 11 Oct 2017
Posts: 1
Re: In a certain class of 5 students, the average (arithmetic mean) weight  [#permalink]

### Show Tags

Sent from my ONE E1003 using GMAT Club Forum mobile app
Intern  B
Joined: 22 Mar 2017
Posts: 27
GMAT 1: 680 Q48 V35
Re: In a certain class of 5 students, the average (arithmetic mean) weight  [#permalink]

### Show Tags

Bunuel wrote:

GMAT Club's Fresh Challenge Problem.

In a certain class of 5 students, the average (arithmetic mean) weight of any two students in the group is less than 70 kg. How many students in the class weigh 70 kg or more?

(1) One of the students weighs more than 70 kg.
(2) The median weight of all 5 students is 68 kg.

Only two cases:

1. None of the students is over 70. In that case the average of ANY two students would be assured to be below 70.
2. ONLY ONE of the students is over 70. For example, the average of 71 and 35 is clearly below 70, BUT the average of 71 and 71 is 71 what is not allowed.

S1.

Case 2. Only 1.

SUFF.

S2.

Two students on the right of 68 can be equal to 68 or greater. It can be either case.

INSUFF.

AC: A

-
Intern  S
Joined: 06 Aug 2017
Posts: 22
Location: India
GMAT 1: 660 Q47 V34
Re: In a certain class of 5 students, the average (arithmetic mean) weight  [#permalink]

### Show Tags

1
Statement 1 is sufficient.
Even if one of the student is more than 70, all the other students must weight lesser than 70. (as the average weight of any two students is 70)
Intern  B
Joined: 22 Nov 2017
Posts: 23
Location: United States
Concentration: Technology, Healthcare
Re: In a certain class of 5 students, the average (arithmetic mean) weight  [#permalink]

### Show Tags

Question says mean of any 2 students less than 70. So sum of weights of any 2 students is less than 70. Statement 1 says 1 student is 70 and more. So if we compare other students with this student their weight should be less than 70. So sufficient. Statement 2 says median is 68. So if arrange is ascending order there will be 2 students before and 2 students after 68. Of 2 students who has weight beyond 68 both of them cannot be greater than 70. But we cannot say that either is one is more than 70 or both is between 68 and 70. So not sufficient. So answer is A

Sent from my SAMSUNG-SM-J120A using GMAT Club Forum mobile app
Math Expert V
Joined: 02 Aug 2009
Posts: 8602
Re: In a certain class of 5 students, the average (arithmetic mean) weight  [#permalink]

### Show Tags

1
1
Bunuel wrote:

GMAT Club's Fresh Challenge Problem.

In a certain class of 5 students, the average (arithmetic mean) weight of any two students in the group is less than 70 kg. How many students in the class weigh 70 kg or more?

(1) One of the students weighs more than 70 kg.
(2) The median weight of all 5 students is 68 kg.

Half the problem is solved by the main statement..

Quote:
the average (arithmetic mean) weight of any two students in the group is less than 70 kg

If there are two numbers equal to or above 70, their average will surely be MORE than or equal to 70..
so MAX number above 70 can be ONLY one ..
second possibility is NONE ..

Our statement should be able to give us some info to eliminate any one of the two..

lets see the statements..
(1) One of the students weighs more than 70 kg.
so it gives us ONE as answer
suff
(2) The median weight of all 5 students is 68 kg.
nothing much..
all 68 ... ans 0
66,66,68,70,70.... ans 2
insuff

A
_________________
Math Expert V
Joined: 02 Sep 2009
Posts: 64222
Re: In a certain class of 5 students, the average (arithmetic mean) weight  [#permalink]

### Show Tags

Bunuel wrote:

GMAT Club's Fresh Challenge Problem.

In a certain class of 5 students, the average (arithmetic mean) weight of any two students in the group is less than 70 kg. How many students in the class weigh 70 kg or more?

(1) One of the students weighs more than 70 kg.
(2) The median weight of all 5 students is 68 kg.

_________________
Intern  B
Joined: 06 Oct 2018
Posts: 31
Re: In a certain class of 5 students, the average (arithmetic mean) weight  [#permalink]

### Show Tags

chetan2u wrote:
Bunuel wrote:

GMAT Club's Fresh Challenge Problem.

In a certain class of 5 students, the average (arithmetic mean) weight of any two students in the group is less than 70 kg. How many students in the class weigh 70 kg or more?

(1) One of the students weighs more than 70 kg.
(2) The median weight of all 5 students is 68 kg.

Half the problem is solved by the main statement..

Quote:
the average (arithmetic mean) weight of any two students in the group is less than 70 kg

If there are two numbers equal to or above 70, their average will surely be MORE than or equal to 70..
so MAX number above 70 can be ONLY one ..
second possibility is NONE ..

Our statement should be able to give us some info to eliminate any one of the two..

lets see the statements..
(1) One of the students weighs more than 70 kg.
so it gives us ONE as answer
suff
(2) The median weight of all 5 students is 68 kg.
nothing much..
all 68 ... ans 0
66,66,68,70,70.... ans 2
insuff

A

Hi,

Sorry to bring up a post from a year ago, but I am working through this New Year set and couldn't help but notice something that seems out of place.

Chetan, you gave as an example for Statement 2:

66, 66, 68, 70, 70 --> this would not fit with the restrictions of the problem. If we take ANY TWO students, their average weight should be LESS THAN 70, not less or equal to. If we take the last 2 students, (70 + 70) / 2 = 70 which is not less than 70. Hence, the second to last student should be less than 70 (either 69 or 68).

Statement 2 is insufficient because of the following 2 cases:
1) 68, 68, 68, 68, 68 whereby the answer to the target question is 0 (0 students over 70kg).
2) 66, 66, 68, 68, 71 whereby the answer is 1 student is over 70kg.
GMAT Tutor B
Joined: 07 Nov 2016
Posts: 52
GMAT 1: 760 Q51 V42 Re: In a certain class of 5 students, the average (arithmetic mean) weight  [#permalink]

### Show Tags

Bunuel wrote:

GMAT Club's Fresh Challenge Problem.

In a certain class of 5 students, the average (arithmetic mean) weight of any two students in the group is less than 70 kg. How many students in the class weigh 70 kg or more?

(1) One of the students weighs more than 70 kg.
(2) The median weight of all 5 students is 68 kg.

St 1 : Even in the following case

<70, <70, <70, 70, >70

The average of the highest two is greater than 70, which violates the condition given

So , the only arrangement possible is

<70, <70, <70, <70, >70

Only one student weighs 70 or more

Sufficient

St 2 : The arrangement could be

68,68,68,68,68 or 68,68,68,68,70

Zero students or one student

Not Sufficient

Choice A
_________________
CEO  V
Joined: 03 Jun 2019
Posts: 2899
Location: India
GMAT 1: 690 Q50 V34 WE: Engineering (Transportation)
Re: In a certain class of 5 students, the average (arithmetic mean) weight  [#permalink]

### Show Tags

Bunuel wrote:

GMAT Club's Fresh Challenge Problem.

In a certain class of 5 students, the average (arithmetic mean) weight of any two students in the group is less than 70 kg. How many students in the class weigh 70 kg or more?

(1) One of the students weighs more than 70 kg.
(2) The median weight of all 5 students is 68 kg.

There are only 2 possibilities for students weighing more than 70 kgs = 1 or 0 since for 2 or greater average of 2 students will be greater than 70 kgs.

(1) One of the students weighs more than 70 kg.
This gives us the answer = 1
SUFFICIENT

(2) The median weight of all 5 students is 68 kg.
There may be students equal to 1 or 0 having weight greater than 70 kgs
NOT SUFFICIENT

IMO A
_________________
Kinshook Chaturvedi
Email: kinshook.chaturvedi@gmail.com Re: In a certain class of 5 students, the average (arithmetic mean) weight   [#permalink] 08 Oct 2019, 03:30

# In a certain class of 5 students, the average (arithmetic mean) weight  