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

 It is currently 15 Jul 2018, 23:59

### 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

# A right triangle has sides of a, b, and 11, respectively,

Author Message
TAGS:

### Hide Tags

Manager
Joined: 07 May 2015
Posts: 93
Re: A right triangle has sides of a, b, and 11, respectively, [#permalink]

### Show Tags

24 Jan 2017, 07:07
VeritasPrepKarishma wrote:
neeraj609 wrote:
anceer wrote:
A right triangle has sides of a, b, and 11, respectively, where a and b are both integers. What is the value of (a + b)?

A. 15
B. 57
C. 93
D. 109
E. 121

So if a and b both are integers, then a+b should also be integer. Now we are asked to find the value of (a+b)^2. I started POE. None of the values is a perfect square (which one square root result into a integer, which should be the value of base a+b) EXCEPT 121.

I am pretty sure it cant be that simple, what am i missing here

How do you figure that we are looking for (a + b)^2?
We are looking for the value of (a + b) only.

Actually i reading (a+b)? wrongly as (a+b)^2. Thanks alot!
Manager
Joined: 04 Aug 2015
Posts: 82
Location: India
GMAT 1: 700 Q50 V35
GPA: 3.39
Re: A right triangle has sides of a, b, and 11, respectively, [#permalink]

### Show Tags

24 Jan 2017, 08:38
A right triangle has sides of a, b, and 11, respectively, where a and b are both integers. What is the value of (a + b)?

Case 1: $$a^2 + b^2 = 11^2 = 121$$ (unit digit 1)

Perfect squares end with any one of the following: 0; 1; 4; 9; 6; 5.
To have unit digit 1, we have to use either of the combos: 0 and 1; 6 and 5. But none satisfies. X

Case 2: $$a^2 + 121 = b^2$$

Subcase (a)
=> $$a^2 = b^2 - 121$$
=> $$a^2 = (b+11) (b-11)$$
Since, $$(b+11)$$ is not equal to $$(b-11)$$and also $$(b+11) > (b-11)$$therefore
$$b-11 = 1$$ and $$b+11 = a^2$$
$$b=12$$ and $$a^2=23$$ (a is not a integer) X

Subcase (b)

=> $$121 = b^2 - a^2$$
=> $$(b-a) (b+a) = 121$$
Therefore, $$b-a=1$$ and $$b+a=121$$
Intern
Joined: 21 Mar 2017
Posts: 40
Location: Zimbabwe
Concentration: General Management, Entrepreneurship
GMAT 1: 680 Q45 V38
GMAT 2: 750 Q49 V42
GPA: 3.3
WE: Accounting (Accounting)
Re: A right triangle has sides of a, b, and 11, respectively, [#permalink]

### Show Tags

12 Sep 2017, 09:30
GMATinsight wrote:
anceer wrote:
A right triangle has sides of a, b, and 11, respectively, where a and b are both integers. What is the value of (a + b)?

A. 15
B. 57
C. 93
D. 109
E. 121

The trick for this question is

If the side of a right angle triangle is a prime number then other two sides will be

Second Side = [(Prime)^2 + 1]/2

Third Side = [(Prime)^2 - 1]/2

i.e. for One side = 11

Second Side = (11^2 -1)/2 = (121-1)/2 = 60
Third Side = (11^2 +1)/2 = (121+1)/2 = 61

I hope this helps!

I personally find it an UNSUITABLE question for GMAT... GMAT Doesn't expect such tricks from students.

Bookmarking this post and making a mental note. Definitely worth knowing!
_________________

Kudos if you like my response please

Re: A right triangle has sides of a, b, and 11, respectively,   [#permalink] 12 Sep 2017, 09:30

Go to page   Previous    1   2   [ 23 posts ]

Display posts from previous: Sort by

# 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®.