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

 It is currently 17 Oct 2019, 13:34 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.  ABC is a right angle triangle, which is 90 degree at A.

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

Hide Tags

Math Expert V
Joined: 02 Aug 2009
Posts: 7971
ABC is a right angle triangle, which is 90 degree at A.  [#permalink]

Show Tags

1
1
3 00:00

Difficulty:   55% (hard)

Question Stats: 62% (01:42) correct 38% (01:32) wrong based on 132 sessions

HideShow timer Statistics

ABC is a right angle triangle, which is 90 degree at A. What is the Area of the triangle ABC?

1) AB + AC = 8.
2) The largest side is 5$$\sqrt{2}$$.

_________________

Originally posted by chetan2u on 23 Jan 2016, 22:48.
Last edited by chetan2u on 30 Nov 2017, 06:41, edited 2 times in total.
..
Marshall & McDonough Moderator D
Joined: 13 Apr 2015
Posts: 1685
Location: India
Re: ABC is a right angle triangle, which is 90 degree at A.  [#permalink]

Show Tags

1
Triangle is right angled at A. So BC is the hypotenuse.
Area = 1/2*(AB)*(AC)

St1: AB + AC = 8 --> Not sufficient as we get multiple possibilities for AB and AC

St2: BC = 5*sqrt(2) --> Not sufficient to determine the area

Combining St1 and St2,
AB^2 + AC^2 = BC^2......(1)
AB + AC = 8 and BC = 5*sqrt(2)
Only AB = 7, AC = 1 or AC = 7, AB = 1 satisfies (1). Thus AB*AC = 7. Area can be found out
St1 and St2 together is sufficient

Intern  B
Joined: 27 Dec 2015
Posts: 9
Concentration: Accounting, Economics
Schools: AGSM '18
GPA: 3.02
WE: Analyst (Accounting)
Re: ABC is a right angle triangle, which is 90 degree at A.  [#permalink]

Show Tags

ABC is a right angle triangle, which is 90 degree at A. What is the Area of the triangle ABC?
1) AB + AC = 8.
2) The largest side is 52√.

AB^2 + AC^2 = BC^2......(1)
AB + AC = 8 and BC = 5*sqrt(2)
Only AB = 7, AC = 1 or AC = 7, AB = 1 satisfies (1). Thus AB*AC = 7. Area can be found out
St1 and St2 together is sufficient

_________________
[color=#7cc576][color=#0072bc][/color][/color]
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8009
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: ABC is a right angle triangle, which is 90 degree at A.  [#permalink]

Show Tags

1
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.

ABC is a right angle triangle, which is 90 degree at A. What is the Area of the triangle ABC?

1) AB + AC = 8.
2) The largest side is 5 √ 2

When you modify the original condition and the question, for the right angle triangle, there are 2 variables(the base line and height), which should match with the number of equations. So you need 2 equations. For 1) 1equation, for 2) 1 equation, which is likely to make C the answer.
When 1) & 2), they become AB^2+AC^2=(5√2)^2=50, (AB+AC)^2=8^2=64, AB^2+AC^2+2AB*AC=64 → 50+2AB*AC=64, AB*AC/2=7/2, which is unique and sufficient.
Therefore, the answer is C.

--> For cases where we need 2 more equations, such as original conditions with “2 variables”, or “3 variables and 1 equation”, or “4 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 70% chance that C is the answer, while E has 25% chance. These two are the majority. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since C is most likely to be the answer using 1) and 2) separately according to DS definition (It saves us time). Obviously there may be cases where the answer is A, B, D or E.
_________________
Intern  B
Joined: 27 Dec 2015
Posts: 9
Concentration: Accounting, Economics
Schools: AGSM '18
GPA: 3.02
WE: Analyst (Accounting)
Re: ABC is a right angle triangle, which is 90 degree at A.  [#permalink]

Show Tags

ABC is a right angle triangle, which is 90 degree at A. What is the Area of the triangle ABC?
1) AB + AC = 8.
2) The largest side is 52√.

AB^2 + AC^2 = BC^2......(1)
AB + AC = 8 and BC = 5*sqrt(2)
Only AB = 7, AC = 1 or AC = 7, AB = 1 satisfies (1). Thus AB*AC = 7. Area can be found out
St1 and St2 together is sufficient

_________________
[color=#7cc576][color=#0072bc][/color][/color]
Manager  S
Joined: 03 Aug 2015
Posts: 51
Concentration: Strategy, Technology
Schools: ISB '18, SPJ GMBA '17
GMAT 1: 680 Q48 V35 Re: ABC is a right angle triangle, which is 90 degree at A.  [#permalink]

Show Tags

Vyshak wrote:
Triangle is right angled at A. So BC is the hypotenuse.
Area = 1/2*(AB)*(AC)

St1: AB + AC = 8 --> Not sufficient as we get multiple possibilities for AB and AC

St2: BC = 5*sqrt(2) --> Not sufficient to determine the area

Combining St1 and St2,
AB^2 + AC^2 = BC^2......(1)
AB + AC = 8 and BC = 5*sqrt(2)
Only AB = 7, AC = 1 or AC = 7, AB = 1 satisfies (1). Thus AB*AC = 7. Area can be found out
St1 and St2 together is sufficient

Understood...But when similar question with different Question is given....I have to try with the different no's and if i get two pairs solving the equation, then i should choose 'E'.

Pls correct if my understanding is wrong.

Thanks,
A CEO  S
Joined: 20 Mar 2014
Posts: 2597
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44 GPA: 3.7
WE: Engineering (Aerospace and Defense)
Re: ABC is a right angle triangle, which is 90 degree at A.  [#permalink]

Show Tags

ArunpriyanJ wrote:

Understood...But when similar question with different Question is given....I have to try with the different no's and if i get two pairs solving the equation, then i should choose 'E'.

Pls correct if my understanding is wrong.

Thanks,
A If there is another question that asks you the area of triangle ABC without telling you which one is the right angle, then yes, there is a high probability that E will be the answer. You have to take it on a case by case basis.

Hope this helps.
Intern  B
Joined: 10 Oct 2017
Posts: 8
Location: United States (GA)
Concentration: Entrepreneurship, Economics
GMAT 1: 700 Q47 V39 GMAT 2: 670 Q43 V40 GPA: 3.43
Re: ABC is a right angle triangle, which is 90 degree at A.  [#permalink]

Show Tags

Why isn't the answer B? If the longest side (hypotenuse) is 5sq.rt.2, then wouldn't that make the other 2 sides 5 and 5?
Math Expert V
Joined: 02 Aug 2009
Posts: 7971
Re: ABC is a right angle triangle, which is 90 degree at A.  [#permalink]

Show Tags

meganbailey wrote:
Why isn't the answer B? If the longest side (hypotenuse) is 5sq.rt.2, then wouldn't that make the other 2 sides 5 and 5?

hi

there will be numerous ways /triangles where hypotenuse is $$5\sqrt{2}$$..
$$a^2+b^2=(5\sqrt{2})^2......a^2+b^2=50$$
say a is 7, b will be 1
a is 6, b will be $$\sqrt{50-36}=\sqrt{24}=2\sqrt{6}$$

hope it helps
_________________
Non-Human User Joined: 09 Sep 2013
Posts: 13244
Re: ABC is a right angle triangle, which is 90 degree at A.  [#permalink]

Show Tags

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________ Re: ABC is a right angle triangle, which is 90 degree at A.   [#permalink] 01 Mar 2019, 11:16
Display posts from previous: Sort by

ABC is a right angle triangle, which is 90 degree at A.

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne  