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

 It is currently 22 Sep 2018, 13:58

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

For a given triangle with sides x,3x and 24, what is the

Author Message
TAGS:

Hide Tags

Verbal Forum Moderator
Joined: 10 Oct 2012
Posts: 614
For a given triangle with sides x,3x and 24, what is the  [#permalink]

Show Tags

01 Aug 2013, 03:37
4
1
00:00

Difficulty:

85% (hard)

Question Stats:

49% (01:12) correct 51% (01:30) wrong based on 149 sessions

HideShow timer Statistics

For a given triangle with sides x,3x and 24, what is the value of the perimeter?

I. (x-3)(x-10) = 0

II.The perimeter is a perfect square.

Source: My own.

_________________
VP
Status: Far, far away!
Joined: 02 Sep 2012
Posts: 1086
Location: Italy
Concentration: Finance, Entrepreneurship
GPA: 3.8
Re: For a given triangle with sides x,3x and 24, what is the  [#permalink]

Show Tags

01 Aug 2013, 04:47
6
2
Rule for triangles: the sum of two sides must be grater than the third side.

For a given triangle with sides x,3x and 24, what is the value of the perimeter?

I. $$(x-3)(x-10) = 0$$
So x can be 3, and the sides would be $$3,9,24$$ <== this is not a triangle as $$3+9<24$$.
Or x can be 10, and the sides would be $$10,30,24$$ <== this is a legit triangle.
Sufficient

II.The perimeter is a perfect square.
Applying the rule we get
$$3x+x>24$$ or $$x>6$$
$$24+3x>x$$ or $$12+2x>0$$ (this is irrelevant as it's always true-x must be positive)
$$24+x>3x$$ or $$12>x$$. So $$12>x>6$$ and the perimeter will range from
if $$x=12$$, $$P=72$$ - if $$x=6$$ $$P=48$$.
Between 48 and 72 there are the following perfect squares: $$49,64$$. Thus x could have two values, and the perimeter would change.
Not sufficient
_________________

It is beyond a doubt that all our knowledge that begins with experience.

Kant , Critique of Pure Reason

Tips and tricks: Inequalities , Mixture | Review: MGMAT workshop
Strategy: SmartGMAT v1.0 | Questions: Verbal challenge SC I-II- CR New SC set out !! , My Quant

Rules for Posting in the Verbal Forum - Rules for Posting in the Quant Forum[/size][/color][/b]

General Discussion
Manager
Joined: 22 Apr 2013
Posts: 82
Re: For a given triangle with sides x,3x and 24, what is the  [#permalink]

Show Tags

01 Aug 2013, 04:08
mau5 wrote:
For a given triangle with sides x,3x and 24, what is the value of the perimeter?

I. (x-3)(x-10) = 0

II.The perimeter is a perfect square.

OA after some discussion.

From I X = 3 or X = 10, Plugging into stem- 3 + 9 + 24 = 36 or 10 + 30 + 24 = 64...not sufficient

From II...not enough info

I + II both potential answers are perfect squares, not sufficient..
_________________

I do not beg for kudos.

Intern
Joined: 21 Oct 2003
Posts: 1
Location: usa
Re: For a given triangle with sides x,3x and 24, what is the  [#permalink]

Show Tags

03 Aug 2013, 08:08
mau5 wrote:
For a given triangle with sides x,3x and 24, what is the value of the perimeter?

I. (x-3)(x-10) = 0

II.The perimeter is a perfect square.

Source: My own.

I is sufficient- it is clear
II x+3x+24=A*2
4x+24=A*2
4(X+6)=A*2
2*2 (X+6)= A*2
solution are x = 3, 10, 19, 30, 43...
for x=3 sides would be 3, 9, 24, but 3+9<24 can not be sides of triangle
x=10 sides would be 10, 30, 24 and 10+24>30 , x can be 10
x=19 sides would be 19, 57, 24 but 19+24<57 , x can not be 19
x=30, sides would be 30,90, 24 but 30+24<90 , x can not be 30
So from II statement x is only 10
Verbal Forum Moderator
Joined: 10 Oct 2012
Posts: 614
Re: For a given triangle with sides x,3x and 24, what is the  [#permalink]

Show Tags

03 Aug 2013, 08:16
bboev wrote:
mau5 wrote:
For a given triangle with sides x,3x and 24, what is the value of the perimeter?

I. (x-3)(x-10) = 0

II.The perimeter is a perfect square.

Source: My own.

I is sufficient- it is clear
II x+3x+24=A*2
4x+24=A*2
4(X+6)=A*2
2*2 (X+6)= A*2
solution are x = 3, 10, 19, 30, 43...
for x=3 sides would be 3, 9, 24, but 3+9<24 can not be sides of triangle
x=10 sides would be 10, 30, 24 and 10+24>30 , x can be 10
x=19 sides would be 19, 57, 24 but 19+24<57 , x can not be 19
x=30, sides would be 30,90, 24 but 30+24<90 , x can not be 30
So from II statement x is only 10

You are assuming that x can only be an integer. you get a perfect square for $$x = \frac{25}{4}$$ and forms a valid triangle.
_________________
Manager
Joined: 06 Jul 2013
Posts: 99
GMAT 1: 620 Q48 V28
GMAT 2: 700 Q50 V33
Re: For a given triangle with sides x,3x and 24, what is the  [#permalink]

Show Tags

03 Aug 2013, 08:23
i - sufficient. i think that is easy
ii - 24+x > 3X
So X < 12
and x+3x>24 then X > 6
24+4X perfect square x can only 10
Sufficient

So D
Verbal Forum Moderator
Joined: 10 Oct 2012
Posts: 614
Re: For a given triangle with sides x,3x and 24, what is the  [#permalink]

Show Tags

03 Aug 2013, 08:28
AMITAGARWAL2 wrote:
i - sufficient. i think that is easy
ii - 24+x > 3X
So X < 12
and x+3x>24 then X > 6
24+4X perfect square x can only 10
Sufficient

So D

Nope.Please refer to the post above.

Thanks.
_________________
Senior Manager
Joined: 10 Jul 2013
Posts: 315
Re: For a given triangle with sides x,3x and 24, what is the  [#permalink]

Show Tags

05 Aug 2013, 14:21
mau5 wrote:
AMITAGARWAL2 wrote:
i - sufficient. i think that is easy
ii - 24+x > 3X
So X < 12
and x+3x>24 then X > 6
24+4X perfect square x can only 10
Sufficient

So D

Nope.Please refer to the post above.

Thanks.

it's an obvious (A).
because x=3 or x=10 .
for a triangle with such sides (x,3x and 24) it's not possible that x=3. because x+3x>24 have to be true always). so x=10 and we know the perimeter = 4x+24=64
st(2) is not needed at all.
_________________

Asif vai.....

Intern
Joined: 14 Jun 2018
Posts: 4
Re: For a given triangle with sides x,3x and 24, what is the  [#permalink]

Show Tags

05 Jul 2018, 00:44
1
mau5 wrote:
For a given triangle with sides x,3x and 24, what is the value of the perimeter?

I. (x-3)(x-10) = 0

II.The perimeter is a perfect square.

Source: My own.
#From first statement we have one value satisfying triangle's properties..ie x=10
*Strike out BCE. Ans must be A or D
*Now perimeter is 4x+24
#According to statement 2 it must b a perfect square...and because of traingles properties x must b greater than equals to 7 and less than 12(PROPERTY OF TRIANGLE I M TALKING ABOUT IS THAT SUM OF ANY TWO SIDES IS ALWAYS GREATER THAN THE THIRD ONE)
*4x+24= 64 is only condition in which x lies b/w 7 and 12(7 inclusive)
**SO ANS IS (D)
I ASSUMED THAT IS AN INTEGER

Sent from my Redmi Note 4 using GMAT Club Forum mobile app
Director
Joined: 20 Feb 2015
Posts: 733
Concentration: Strategy, General Management
Re: For a given triangle with sides x,3x and 24, what is the  [#permalink]

Show Tags

05 Jul 2018, 01:01
mau5 wrote:
For a given triangle with sides x,3x and 24, what is the value of the perimeter?

I. (x-3)(x-10) = 0

II.The perimeter is a perfect square.

Source: My own.

sides x, 3x and 24
so
x+3x > 24
4x > 24
x > 6

1.x=3,x=10
since x is > 6 , x=10 sufficient

2. x+3x+24 = a^2
4x+24=perfect square
perfect squares > 24 are
36 for which 4x=12 , x =3
but x should be > 6
49 for which 4x=25 , x=6.25
64 for which 4x=30 , x=7.50
...
insufficient

A it is !!
Re: For a given triangle with sides x,3x and 24, what is the &nbs [#permalink] 05 Jul 2018, 01:01
Display posts from previous: Sort by

For a given triangle with sides x,3x and 24, what is the

Events & Promotions

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.