GMAT Problem Solving Discussions

[krsh.vik]

Originally Posted by Sailor

Bingo!
You are right.
Please post your explanation.

Thanks

use the property tangents from an external point are equal
sides are x+6 x+8 and 14
area = rs s - semiperimeter r = inradius

[sharad_1980]

Originally Posted by Sailor

Hi all,
Pls help with this question.

A triangle ABC is drawn to circumscribe a circle of radius 4 cm such that the segments BD and DC into which BC is divided by the point of contact D are of lengths 8 cm and 6 cm respectively. Find the sides AB and AC.
Attachment 6346

Regards

See the above file once X=7
sides are 7+6=13
7+8=15

[ChivaS]

Originally Posted by sharad_1980

See the above file once X=7
sides are 7+6=13
7+8=15

Sharad, good explaination that the lengths of tangents from external point will be same.
So, the sides have to be x+6, x+8 ;

but then the later explaination in the solution diagram assumes that the extension of the
angular bisectors are going to become parpenticulars onto the apposite side, which may not hold good ( just think about it , perpenticulars are different from bisectors ).

This qn could be solved by Area= rs

Also from the answer choices we can eliminate the combinations that don't differ
by 2 , and the order given ( which one is shorter/longer ).

Cheers,
ChivaS

[sharad_1980]

Originally Posted by ChivaS

but then the later explaination in the solution diagram assumes that the extension of the
angular bisectors are going to become parpenticulars onto the apposite side, which may not hold good ( just think about it , perpenticulars are different from bisectors ).

This qn could be solved by Area= rs

Also from the answer choices we can eliminate the combinations that don't differ
by 2 , and the order given ( which one is shorter/longer ).

Cheers,
ChivaS

Nooooo Noooooo Noooooo

I think diagram was a bit unclear and u did not get me. The two lines are different.
one is the perp from center to the side. which is a tangent and hence angle is 90.
second joins center to the vertex and hence is the angle bisector.
Tan are taken for smaller triangles
though may seem same from the diagram but are different lines.

hope that clarifies . Please state if there is stilll a confusion.

[ChivaS]

Hey Puys, one small DS question,
Give it a try , I will post the answer with explaination by evening today!



If the square root of the product of three distinct positive integers is equal to the largest of the three numbers, what is the product of the two smaller numbers?

(1) The largest number of the three distinct numbers is 12.

(2) The average (arithmetic mean) of the three numbers is 20/3


A, B , C , D , E are,
as per DS standard answer choices. (1 alone, 2 along etc....)

[mealiennothuman]

Originally Posted by ChivaS

Hey Puys, one small DS question,
Give it a try , I will post the answer with explaination by evening today!



If the square root of the product of three distinct positive integers is equal to the largest of the three numbers, what is the product of the two smaller numbers?

(1) The largest number of the three distinct numbers is 12.

(2) The average (arithmetic mean) of the three numbers is 20/3


A, B , C , D , E are,
as per DS standard answer choices. (1 alone, 2 along etc....)

It is clearly mentioned that the integers are positive. So since the square root is equal to the largest of the numbers, the product of the other two has to be equal to the largest number.

So (1) is enough to answer this question.

Now, the only combination x,y,z such that x+y+z=20 and xy=z is x=2,y=6,z=12. I am not able to think of any other combination.
Hence (2) alone is also enough.

Hence the answer is "Can be answered using either one of the two." (D)

[ChivaS]

Originally Posted by ChivaS

Hey Puys, one small DS question,
Give it a try , I will post the answer with explaination by evening today!



If the square root of the product of three distinct positive integers is equal to the largest of the three numbers, what is the product of the two smaller numbers?

(1) The largest number of the three distinct numbers is 12.

(2) The average (arithmetic mean) of the three numbers is 20/3


A, B , C , D , E are,
as per DS standard answer choices. (1 alone, 2 along etc....)

As told ealier , posting the explaination for this question :

If you call the three numbers x, y and z, and let x be the biggest, then the question tells you that x = square root of the product of x, y and z. If you square both sides of this equation you get:

x² = xyz (which gets rid of the square root). Dividing both sides by x gives you:

x = yz.

So, if you can find a value for x, you can answer the question, which ONLY asks for 'the product of the smaller numbers'.

Statement (1) tells you that x is 12, plug that into x = yz and you get: yz = 12 (because the question asks "what is the product of the two smaller numbers?", this is what you are looking for and it is sufficient.)

Statement (2) tells you that (x + y + z)/3 = 20/3. Now, if x = yz and x + y + z = 20, then the only possibility is (2,6) and (12) as the (y, z) and (x). Every other combination of three integers summing up to 20 fails. 1,2,17; 1,3,16; 1,4,15; 1,5,14; 1,6,13; 1,7,12; 1,8,11; 1,9,10; 2,3,15; 2,4,14; 2,5,13; 2,6,12; 2,7,11; 2,8,10; 3,4,13; 3,5,12; 3,6,11; 3,7,10; 3,8,9; 4,5,11; 4,6,10; 4,7,9; 5,6,9; 5,7,8; and that's the end of the possible combinations of three integers whose sum equals 20. The only combination that works is 2,6,12. If it were 1,9,10, then yz would not equal x. If it were any other combination, such as 5,7,8, then yz would not equal x. The only solution is 2,6,12. This means that yes, Statement 2 is sufficient because the product of yz is 12. Note: this is an extremely hard question that few students get right.

Since both statements are sufficient, the answer is D.

Anyother time saving tips/tricks are welcome.

[ChivaS]

Puys ! one more DS qn!


x > y > 0. If x and y are integers, is y even?

(1) x - y = 1

(2) 2x + y = 32


A,B,C,D,E , just the usual DS answer choices ( 1 alone, 2 alone etc ... )


Cheers,
ChivaS

[dumbJoe]

Originally Posted by ChivaS

Puys ! one more DS qn!


x > y > 0. If x and y are integers, is y even?

(1) x - y = 1

(2) 2x + y = 32


A,B,C,D,E , just the usual DS answer choices ( 1 alone, 2 alone etc ... )


Cheers,
ChivaS

ans -> B
2x has to be even and for sum to be even y has to be even. A just gives the difference. doesnt tell things either way

[mealiennothuman]

Originally Posted by ChivaS

Puys ! one more DS qn!


x > y > 0. If x and y are integers, is y even?

(1) x - y = 1

(2) 2x + y = 32


A,B,C,D,E , just the usual DS answer choices ( 1 alone, 2 alone etc ... )


Cheers,
ChivaS

(1) doesnt tell us anything.

(2) is enough to answer the question as (32 - 2x) = 2(16-x) has to be even.

Hence (B).