GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 18 Nov 2019, 04:47 ### 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.  # The sum of five integers is 999, while the sum of their squares is X.

Author Message
TAGS:

### Hide Tags

Manager  G
Joined: 17 Mar 2015
Posts: 86
The sum of five integers is 999, while the sum of their squares is X.  [#permalink]

### Show Tags

6 00:00

Difficulty:   95% (hard)

Question Stats: 28% (02:13) correct 73% (02:08) wrong based on 57 sessions

### HideShow timer Statistics

The sum of five integers is 999, while the sum of their squares is X. Which of the following statements is true.

A. X is never greater than 1,001,001
B. X is never less than 299794
C. X is never less than 199,601
D. X can never be a perfect square.
E. None of the above.
VP  P
Joined: 07 Dec 2014
Posts: 1221
Re: The sum of five integers is 999, while the sum of their squares is X.  [#permalink]

### Show Tags

prince00113 wrote:
the sum of five integers is 999, while the sum of their squares is X. Which of the following statements is true.

A. X is never greater than 1,001,001
B. X is never less than 299794
C. X is never less than 199,601
D. X can never be a perfect square.
E. None of the above.]

999/5=199.8 arithmetic mean
let the five integers=200+200+200+200+199=999
X=199,601
X can never be less than this
C
Senior Manager  P
Joined: 27 Dec 2016
Posts: 309
Re: The sum of five integers is 999, while the sum of their squares is X.  [#permalink]

### Show Tags

Can anyone please explain why option A is incorrect?
Senior PS Moderator V
Joined: 26 Feb 2016
Posts: 3308
Location: India
GPA: 3.12
Re: The sum of five integers is 999, while the sum of their squares is X.  [#permalink]

### Show Tags

csaluja wrote:
Can anyone please explain why option A is incorrect?

If the 5 integers are 1499,-200,-100,-100,-100(the sum is 999)
But the sum of the squares of the numbers is definitely greater than 1001001

That is the reason why A is incorrect as X is greater than 1001001

_________________
You've got what it takes, but it will take everything you've got
Math Expert V
Joined: 02 Aug 2009
Posts: 8182
The sum of five integers is 999, while the sum of their squares is X.  [#permalink]

### Show Tags

prince00113 wrote:
The sum of five integers is 999, while the sum of their squares is X. Which of the following statements is true.

A. X is never greater than 1,001,001
B. X is never less than 299794
C. X is never less than 199,601
D. X can never be a perfect square.
E. None of the above.

The question points towards looking for ranges..

Few points therefore..
1) B can be thrown immediately, as B constitutes the range of C..
2) Max value :-
Nothing has been said about integers being POSITIVE or NEGATIVE.
So the highest value of X can be INFINITY upwards.
Say integers are, 1000000.....n times., -10000..n times, 999, 0, 0
Here sum will be 0, but sum of squares can be anything..
Eliminate A
3) Min value :-
Min value will be when all numbers are smallest possible. And this will happen when all are close by.. here all will be ~ 200...
So Sum <5*(200)^2......<5*40000....<200000..
Here C fits in..
_________________
Director  P
Joined: 31 Jul 2017
Posts: 510
Location: Malaysia
GMAT 1: 700 Q50 V33 GPA: 3.95
WE: Consulting (Energy and Utilities)
Re: The sum of five integers is 999, while the sum of their squares is X.  [#permalink]

### Show Tags

prince00113 wrote:
The sum of five integers is 999, while the sum of their squares is X. Which of the following statements is true.

A. X is never greater than 1,001,001
B. X is never less than 299794
C. X is never less than 199,601
D. X can never be a perfect square.
E. None of the above.

This can be best solved by taking all the numbers distributed equally.

$$a= b= c = d = e = 200$$
$$a^2 + b^2 + c^2 + d^2 + e^2 > 200,000$$
As it asks for minimum value $$X > 199, 601$$ (Please note that I took the value of e = 200 just to simplify calculation, however it should be 199).
_________________
If my Post helps you in Gaining Knowledge, Help me with KUDOS.. !! Re: The sum of five integers is 999, while the sum of their squares is X.   [#permalink] 01 Feb 2018, 22:58
Display posts from previous: Sort by

# The sum of five integers is 999, while the sum of their squares is X.  