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

 It is currently 21 Oct 2018, 16:40

### 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

# Is the length of a side of square S greater than the length of a side

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 50009
Is the length of a side of square S greater than the length of a side  [#permalink]

### Show Tags

27 Dec 2015, 10:48
00:00

Difficulty:

35% (medium)

Question Stats:

77% (01:45) correct 23% (01:57) wrong based on 113 sessions

### HideShow timer Statistics

Is the length of a side of square S greater than the length of a side of equilateral triangle T ?

(1) The sum of the lengths of a side of S and a side of T is 22.
(2) The ratio of the perimeter of square S to the perimeter of triangle T is 5 to 6.

_________________
Current Student
Joined: 29 Jul 2015
Posts: 64
Location: Australia
GMAT 1: 680 Q49 V33
GPA: 3.25
WE: Business Development (Energy and Utilities)
Re: Is the length of a side of square S greater than the length of a side  [#permalink]

### Show Tags

29 Dec 2015, 17:06
Let the side of the Square S = x and side of the equilateral triangle T = y.

Question : x>y? or can be rephrased to say $$\frac{x}{y} > 1$$ (x and y cant be neg).

Statement 1:

x + y = 22.

Lets test values:

11 + 11 = 22, in this case the answer to the question is NO
12 + 10 = 22. in this case the answer to the question is YES.

2 different answers and hence Statement 1 is insufficient.

Statement 2:
Perimeter of the square = 4x
Perimeter of the triangle = 3y

$$\frac{4x}{3y} = \frac{5}{6}$$

$$\frac{x}{y} = \frac{5}{6} * \frac{3}{4}$$ This is clearly less than 1.

Hence $$\frac{x}{y} < 1$$ or x<y. Sufficient.

Manager
Joined: 07 May 2015
Posts: 175
Location: India
GMAT 1: 660 Q48 V31
GPA: 3
Re: Is the length of a side of square S greater than the length of a side  [#permalink]

### Show Tags

03 Jan 2016, 04:54
Statement 1: s+t =22
insufficient
Statement 2: 4S/3T = 5/6
S/T = 5/8 which is less than 1
thus
S<T
Sufficient

Ans: B
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 6390
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: Is the length of a side of square S greater than the length of a side  [#permalink]

### Show Tags

04 Jan 2016, 04:25
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

Is the length of a side of square S greater than the length of a side of equilateral triangle T ?

(1) The sum of the lengths of a side of S and a side of T is 22.
(2) The ratio of the perimeter of square S to the perimeter of triangle T is 5 to 6.

In general, when you suppose a:b=2:3 when it comes to ratio, you don't know how big 'b' is but you know that b>a. That is, you can compare a size with the ratio. Also, when one con is number and the other con is ratio(percent), percent is most likely to be an answer.
In the question, it asks if the length a side of square is greater than the length of a side of equilateral triangle. In 2), the question asks the ratio. So, suppose the sum of the lengths of a side of square 5k and the sum of the lengths of a side of equilateral triangle 6k. Then the length of one side of square is 5k/4=1.25k and the length of one side of equilateral triangle is 6k/3=2k, which is 1.25k<2k. So, it is no and sufficient. Therefore, the answer is B. Just like this question, when one con is number and the other conis ratio, you have to pay attention to ratio.

 from con 1) and con 2), if one of the conditions is given by numbers and the other is given by ratio (percent,fraction), then the condition with ratio (percent,fraction) value has higher chance of being the answer.
_________________

MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only \$99 for 3 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"

Board of Directors
Joined: 17 Jul 2014
Posts: 2657
Location: United States (IL)
Concentration: Finance, Economics
GMAT 1: 650 Q49 V30
GPA: 3.92
WE: General Management (Transportation)
Re: Is the length of a side of square S greater than the length of a side  [#permalink]

### Show Tags

09 Mar 2017, 17:46
Bunuel wrote:
Is the length of a side of square S greater than the length of a side of equilateral triangle T ?

(1) The sum of the lengths of a side of S and a side of T is 22.
(2) The ratio of the perimeter of square S to the perimeter of triangle T is 5 to 6.

statement 1 alone doesn't give much info...
say side of square is "s", and side of triangle is "a"
we have: 4s+3a=22. we can't solve any further.

statement 2, on the contrary...gives sufficient information.
4s/3a = 5/6
8s=3a
we can find the ratio for s/a and see which one is bigger, but clearly, it says that side of the triangle is much bigger.

statement 2 is sufficient.
Re: Is the length of a side of square S greater than the length of a side &nbs [#permalink] 09 Mar 2017, 17:46
Display posts from previous: Sort by