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Is the area of the right angled triangle ABC>25?

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Is the area of the right angled triangle ABC>25?  [#permalink]

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Updated on: 05 Mar 2016, 04:05
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65% (hard)

Question Stats:

53% (01:44) correct 47% (01:45) wrong based on 121 sessions

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Is the area of the right angled triangle ABC>25?

1) AC = 6
2) AB = 10

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Originally posted by seesharp on 05 Mar 2016, 02:42.
Last edited by ENGRTOMBA2018 on 05 Mar 2016, 04:05, edited 1 time in total.
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Joined: 02 Aug 2009
Posts: 7334
Re: Is the area of the right angled triangle ABC>25?  [#permalink]

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05 Mar 2016, 02:54
4
1
seesharp wrote:
Is the area of the right angled triangle ABC>25?

1) AC = 6
2) AB = 10

Hi,
whenever we see a restrictions, <,>, atleast etc, more often than not, the answer is possible through a statement..

1) AC = 6
Since, one of the sides is 6, the other can take any value
Insuff..

2) AB = 10
It is given that hyp is 10..
An isosceles right angle triangle will have max area..
so with Hyp as 10 , the max area possible is when the other two sides are equal..
so each side = Hyp/$$\sqrt{2}$$=10/$$\sqrt{2}$$..
area = 1/2 * 10/$$\sqrt{2}$$*10/$$\sqrt{2}$$
=>100/4=25..
so max area possible is 25..
so teh area of ABC can never be >25..
Suff

ANS B

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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html
4) Base while finding % increase and % decrease : https://gmatclub.com/forum/percentage-increase-decrease-what-should-be-the-denominator-287528.html

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Joined: 05 Jul 2014
Posts: 6
Re: Is the area of the right angled triangle ABC>25?  [#permalink]

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05 Mar 2016, 03:10
chetan2u wrote:
seesharp wrote:
Is the area of the right angled triangle ABC>25?

1) AC = 6
2) AB = 10

Hi,
whenever we see a restrictions, <,>, atleast etc, more often than not, the answer is possible through a statement..

1) AC = 6
Since, one of the sides is 6, the other can take any value
Insuff..

2) AB = 10
It is given that hyp is 10..
An isosceles right angle triangle will have max area..
so with Hyp as 10 , the max area possible is when the other two sides are equal..
so each side = Hyp/$$\sqrt{2}$$=10/$$\sqrt{2}$$..
area = 1/2 * 10/$$\sqrt{2}$$*10/$$\sqrt{2}$$
=>100/4=25..
so max area possible is 25..
so teh area of ABC can never be >25..
Suff

ANS B

Thanks, so you assumed the triangle to be an isosceles to give the maximum possible area. That is great. How about if statement 2 was AB=11? What would the answer be then? C or E?
Math Expert
Joined: 02 Aug 2009
Posts: 7334
Re: Is the area of the right angled triangle ABC>25?  [#permalink]

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05 Mar 2016, 03:13
seesharp wrote:
chetan2u wrote:
seesharp wrote:
Is the area of the right angled triangle ABC>25?

1) AC = 6
2) AB = 10

Hi,
whenever we see a restrictions, <,>, atleast etc, more often than not, the answer is possible through a statement..

1) AC = 6
Since, one of the sides is 6, the other can take any value
Insuff..

2) AB = 10
It is given that hyp is 10..
An isosceles right angle triangle will have max area..
so with Hyp as 10 , the max area possible is when the other two sides are equal..
so each side = Hyp/$$\sqrt{2}$$=10/$$\sqrt{2}$$..
area = 1/2 * 10/$$\sqrt{2}$$*10/$$\sqrt{2}$$
=>100/4=25..
so max area possible is 25..
so teh area of ABC can never be >25..
Suff

ANS B

Thanks, so you assumed the triangle to be an isosceles to give the maximum possible area. That is great. How about if statement 2 was AB=11? What would the answer be then? C or E?

The answer will be Statement 2 will be INSUFF and answer will be C..
But the trap lies in assuming C to be the answer without trying for MAX possible AREA..
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html
4) Base while finding % increase and % decrease : https://gmatclub.com/forum/percentage-increase-decrease-what-should-be-the-denominator-287528.html

GMAT Expert

Math Expert
Joined: 02 Aug 2009
Posts: 7334
Re: Is the area of the right angled triangle ABC>25?  [#permalink]

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05 Mar 2016, 03:19
seesharp wrote:
chetan2u wrote:
seesharp wrote:
Is the area of the right angled triangle ABC>25?

1) AC = 6
2) AB = 10

Hi,
whenever we see a restrictions, <,>, atleast etc, more often than not, the answer is possible through a statement..

1) AC = 6
Since, one of the sides is 6, the other can take any value
Insuff..

2) AB = 10
It is given that hyp is 10..
An isosceles right angle triangle will have max area..
so with Hyp as 10 , the max area possible is when the other two sides are equal..
so each side = Hyp/$$\sqrt{2}$$=10/$$\sqrt{2}$$..
area = 1/2 * 10/$$\sqrt{2}$$*10/$$\sqrt{2}$$
=>100/4=25..
so max area possible is 25..
so teh area of ABC can never be >25..
Suff

ANS B

Thanks, so you assumed the triangle to be an isosceles to give the maximum possible area. That is great. How about if statement 2 was AB=11? What would the answer be then? C or E?

Hi seesharp,

the LOGIC, which may help you in some other Qs too, is..
Given sum of any two numbers, the product will be MAX when the two numbers are same..
Example SUM=a+b =10..
max product ab = 10/2 * 10/2= 25..
that is a aand b are 5 each..
try any combination of a and b, product will not >25..
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html
4) Base while finding % increase and % decrease : https://gmatclub.com/forum/percentage-increase-decrease-what-should-be-the-denominator-287528.html

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Re: Is the area of the right angled triangle ABC>25?  [#permalink]

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05 Mar 2016, 04:18
seesharp wrote:
Is the area of the right angled triangle ABC>25?

1) AC = 6
2) AB = 10

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Is the area of the right angled triangle ABC>25?  [#permalink]

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05 Mar 2016, 11:08
chetan2u wrote:

The answer will be Statement 2 will be INSUFF and answer will be C..
But the trap lies in assuming C to be the answer without trying for MAX possible AREA..

Yes, its a C-trap question, Its creator knows that students will not try max area. But why B would be insuff if AB=11? why looking at value 10 of AB makes us look for max area. if its about Pythagorean triplets then we can consider the same for value 6 of AC and choice A would be correct too? Please explain chetan2u
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Re: Is the area of the right angled triangle ABC>25?  [#permalink]

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05 Mar 2016, 11:55
HKD1710 wrote:
chetan2u wrote:

The answer will be Statement 2 will be INSUFF and answer will be C..
But the trap lies in assuming C to be the answer without trying for MAX possible AREA..

Yes, its a C-trap question, Its creator knows that students will not try max area. But why B would be insuff if AB=11? why looking at value 10 of AB makes us look for max area. if its about Pythagorean triplets then we can consider the same for value 6 of AC and choice A would be correct too? Please explain chetan2u

Its better if you look at a few cases when AB=11.

Case 1: it is an iscosceles right triangle, giving you $$AC=BC=11/\sqrt{2}$$ ---> $$Area = 0.5*11/\sqrt{2}*11/\sqrt{2} = 121/4 > 25$$ but if

Case 2: $$AC=\sqrt{120}$$ and BC =1, you still get AB=11 but in this case, $$Area = 0.5*\sqrt{120}*1$$ <25

This is the reason why statement 2 of this hypothetical question will not be sufficient.

Hope this helps.
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Re: Is the area of the right angled triangle ABC>25?  [#permalink]

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Re: Is the area of the right angled triangle ABC>25?   [#permalink] 13 Oct 2018, 12:01
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