GMAT Problem Solving Discussions

harneet.m.kaur · July 22, 2008, 4:03pm

hey holy_luv,

Don't you think the question is lil confusing it says "intersecting". Should we consider those points also at which the triangle is just touching the circle but not intersecting it. If not, then the correct answer will be 2,4,6.

@harneet, whats the OA ?

Thats what I thought and so my answer was 2, 4, 6 but the OA - (A) 1,2,3,4,5,6

dopa · July 22, 2008, 4:18pm

harneet.m.kaur Says
Thats what I thought and so my answer was 2, 4, 6 but the OA - (A) 1,2,3,4,5,6

well, from where you got this question ?
hope we don't get any ambiguity in the questions on the G-day...having said that, I am not sure was this really ambiguous or my elementary mind failed to recognise the trick 😉

calendar · July 22, 2008, 4:23pm

I guess the answer is 2 !

msd_2008 · July 23, 2008, 6:11am

@MSD,

Following are my answers -

1. E
2. C
3. C
4. Not sure
5. A

What are the correct anwers ? If mine are correct, I'll post the explanations.

The OA's are
1. A
2. C
3. E
4. C
5. A

Please post the explanations for those answers which you've got correct.

Regards
MSD

harneet.m.kaur · July 23, 2008, 10:10am

John's employer is sponsoring a major golf tournament. John's boss has asked him to play in a Pro-Am event prior to the tournament. There are 140 professionals and amateurs playing the Pro-Am. If the ratio of professionals to amateurs is 2 to 5, how many professionals are playing in the Pro-Am?

My answer is 40 but that's certainly not correct. 140 is the total in the ratio 2:5. Thus 40 and 100 should be number. but thats not an option. can some one help

harneet.m.kaur · July 23, 2008, 11:08am

What is the value of (x + y)/x, if the ratio of x:y is 5:4?

Lord - Simple problems are getting difficult. OA - 2. Can some one xplain ?

harneet.m.kaur · July 23, 2008, 11:39am

ankitgarg20 Says
From where are u quoting these questions? Are you sure you takin them from a reliable source? Coz, even for this question answer shud be 1) 9/5 & not 7/3....

Yup the answers seem skewed. Its from a website called test and tutors. My answer was 9/5. 😉 Thanks for the confirmation

harneet.m.kaur · July 23, 2008, 11:51am

Another one -

The front cover of Billy's cereal box, a perfect rectangle, has an area of 36 cm and a perimeter of 26 cm. One of the side of the ceral box fron cover has a length of how much?

harneet.m.kaur · July 23, 2008, 12:05pm

The areas of triangle X and rectangle Y both equal 3200. If rectangle Y has a width of 80, and the height of triangle X is equal to the length of rectangle Y, what is the length of the base of triangle X?

640
320
160
80
40

In a problem like this , will you consider the length of the rectangle as height or the breadth ? The answers are different depending upon what you consider the height. Pls suggest the approach that should be applied to such problems

harneet.m.kaur · July 23, 2008, 2:24pm

If square A's diagonal is half of square B's diagonal, what is the ratio of the area of square B to the area of square A?

My analysis - 2A^2 = 1/2*2B^2. Therefore the ratios of area of B to A should be 2:1. Again, thats not an option. Can anybody confirm.

harneet.m.kaur · July 23, 2008, 2:30pm

The diagonal of Red Square is 10 m. The diagonal of Tianmen Square is 12 m. How many square meters greater is the area of the Tianmen Square than Red Square?

Another one - For red square the diagonal = 10 m so the area is 5m
For Tianmen square the diagonal = 12m so area is 6m. May be I am mising a logic

holy_luv · July 23, 2008, 2:42pm

The diagonal of Red Square is 10 m. The diagonal of Tianmen Square is 12 m. How many square meters greater is the area of the Tianmen Square than Red Square?
22
16
12
11
4
Another one - For red square the diagonal = 10 m so the area is 5m
For Tianmen square the diagonal = 12m so area is 6m. May be I am mising a logic

ummm??
hey area of a square = side^2 = (diagonal/sqrt(2))^2
in our case...area of red square=(10/sqrt(2))^2=50sq m
area of tianmen square=(12/sqrt(2))^2=72sq m
difference=22sqm

holy_luv · July 23, 2008, 2:46pm

If square A's diagonal is half of square B's diagonal, what is the ratio of the area of square B to the area of square A?
4:5
4:1
1:2
2:3
1:4
My analysis - 2A^2 = 1/2*2B^2. Therefore the ratios of area of B to A should be 2:1. Again, thats not an option. Can anybody confirm.

ratio of diagonals=2:1
ratio of area=(diagonal A/diagonal B)^2=4:1

harneet.m.kaur · July 23, 2008, 2:58pm

ummm??
hey area of a square = side^2 = (diagonal/sqrt(2))^2
in our case...area of red square=(10/sqrt(2))^2=50sq m
area of tianmen square=(12/sqrt(2))^2=72sq m
difference=22sqm

Oh yea !! Confused this with the last problem where it said square of the diagonal. Thanks 😃

harneet.m.kaur · July 23, 2008, 3:08pm

ratio of diagonals=2:1
ratio of area=(diagonal A/diagonal B)^2=4:1

Hey - Didnot get this - May be I am missing something elementary. Now my logic is -
Sq A side measures "a". The diagonal square therefore is 2a^2 (Pythagoras thrm a^2+a^2 = 2a^2)
Sq B side measures "b". The diagonal square therefore if 2b^2

Given that = 2a^2 = 1/2 (2b^2)
Ratios of area = b^2 : a^2 = 2:1

:idea: - Pls help point out my error

calendar · July 23, 2008, 4:38pm

another bad method
The area of triangle = (rcosA)(2rSinA)/2
= 1/2 * r^2 *Sin2A
r^2 =1
Sin2A can be maximum of 1
Hence area of the triangle can be max 1/2

inder.14 · July 23, 2008, 6:46pm

Hey - Didnot get this - May be I am missing something elementary. Now my logic is -
Sq A side measures "a". The diagonal square therefore is 2a^2 (Pythagoras thrm a^2+a^2 = 2a^2)
Sq B side measures "b". The diagonal square therefore if 2b^2

Given that = 2a^2 = 1/2 (2b^2)
Ratios of area = b^2 : a^2 = 2:1

:idea: - Pls help point out my error

Lets make it simple
side of square 'A' is a and side of square 'B' is b

diagonal of A = a*(2)^1/2
diagonal of B= b*(2)^1/2
as per given condition
diagonal of A = 1/2* diagonal of B
=> a*(2)^1/2 = 1/2* b*(2)1/2
=> a=b/2
Area of square B =b^2
Area of square A = a^2
now
Area of square B/Area ofsquareA=b^2/a^2 ( now b=2a as solved above)
= (2a)^2/a^2=4/1
hence ratio is 4:1

hope now its clear

srikanth267 · July 23, 2008, 7:28pm

Lets make it simple
side of square 'A' is a and side of square 'B' is b

diagonal of A = a*(2)^1/2
diagonal of B= b*(2)^1/2
as per given condition
diagonal of A = 1/2* diagonal of B
=> a*(2)^1/2 = 1/2* b*(2)1/2
=> a=b/2
Area of square B =b^2
Area of square A = a^2
now
Area of square B/Area ofsquareA=b^2/a^2 ( now b=2a as solved above)
= (2a)^2/a^2=4/1
hence ratio is 4:1

hope now its clear

Side of sq A be a
Hence diagonal measures a(sqrt2)
Similarly side of sq B measures b(sqrt2)
Given a(sqrt2)=1/2
hence b=2a
Ratio of area of sq B to sq A= 4a^2/a^2=4:1

hope this is much simpler n easy to understand......
comments r welcome!!

srikanth267 · July 23, 2008, 7:38pm

The diagonal of Red Square is 10 m. The diagonal of Tianmen Square is 12 m. How many square meters greater is the area of the Tianmen Square than Red Square?
22
16
12
11
4
Another one - For red square the diagonal = 10 m so the area is 5m
For Tianmen square the diagonal = 12m so area is 6m. May be I am mising a logic

side of sq whose diaonal is 10 cm is 5(sqrt2)
side whose diagona; is 12 cm is 6(sqrt2)
Diff of area=72-50=22 sq units

dopa · July 23, 2008, 7:58pm

Need help with the following data sufficiency questions:

A. An integer freater than 1 that is not prime is called composite. If the two digit integer n is greater than 20, is n composite?
1. The tens digit of n is a factor of the units digit of n
2. The tens digit of n is 2

B. If the terms of a sequence are t1, t2, t3......tn what is the value of n?
1. The sum of n terms is 3124
2. The average (arithmatic mean) of n terms is 4

C. In the xy plane, what is the y intercept of Line L
1. The slope of line L is 3 times its y intercept
2. the x intercept of line L is -1/3

D. Of the 60 animals on a certain farm 2/3 are either pigs or cows. how many of the animals are cows?
1. The farm has more than twice as many cows are it has pigs
2. The farm has more than 12 pigs

E. In a typical rectangular coordinate system (I, II, III, IV quadrants), does line K intersect quandrant II?
1. The slope of K is -1/6
2. The Y intercept of K is -6

Regards
MSD

@MSD, here are my explantaions for 1, 2 and 5th :-

1. The number has 2 digits and is greater than 20 so it can be any number between 21 - 99.
Option -A: The tens digit of n is a factor of the units digit of n, that means if tens digit is 2, tens digit could only be 2,4,6,8 making the number as 22,24,26,28 (similar for an odd number at tens place). All of these number are composite. Sufficient.

Option -B: The tens digit of n is 2 that makes n a even number and all even numbers are composite except 2 and n >20. So, n is composite. Sufficient.

Answer is D.

2. We have to find value of n, in other terms we have to find no. of terms in the sequence.

Option -A: Sum of all the terms is 3124 but we dont know as what are the actual values of terms so there are various possible terms which can make sum 3124. Not sufficient.

Option -B: Average of n terms is 4. This information is of no good as we dont know the sum (don't get in the trap and consider sum as 3124, consider B option alone). Not sufficient.

Option A and B simultaneously: Sum = 3124, Average = 4. As we know (Sum of n terms/n = Average) => n = 3124/4 = 781. Sufficient.

Answer is C.

5. does line K intersect quandrant II?

Option -A: All the lines having a negative slope will pass through IInd quadrant as slope = tan (angle made by line K at x axis) and tan is negative in II quadrant. Sufficient.
This can also be solved just by drawing a line having negative slope on rectangular coordinate (please refer figure A in the attached document)

Option -B: Y intercept of line K is negative. A line having negative intercept can or can not pass through II quadrant. Not sufficient
please refer figure B in the attached document for a line having negative intercept on Y but its not passing through II quadrant.

Answer is A.

Regards,
Ashutosh