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DS problems

by gabriel » Wed Apr 18, 2007 11:05 am
guys here are some good DS problems ... try and solve them ..

q.) Train A leaves New York for Boston at 3 PM and travels at the constant speed of 100 mph. An hour later, it passes Train B, which is making the trip from Boston to New York at a constant speed. If Train B left Boston at 3:50 PM and if the combined travel time of the two trains is 2 hours, what time did Train B arrive in New York?
(1) Train B arrived in New York before Train A arrived in Boston.

(2) The distance between New York and Boston is greater than 140 miles.

(A) Statement (1) alone is sufficient, but statement (2) alone is not sufficient.
(B) Statement (2) alone is sufficient, but statement (1) alone is not sufficient.
(C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
(D) Each statement ALONE is sufficient.
(E) Statements (1) and (2) TOGETHER are NOT sufficient.


q.)Last Friday a certain shop sold 3/4 of the sweaters in its inventory. Each sweater sold or $20. What was the total revenue last Friday from the sale of these sweaters?

(1) When the shop opened last Friday, there were 160 sweaters in its inventory.
(2) All but 40 sweaters in the shop’s inventory were sold last Friday.

A Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D EACH Statement ALONE is sufficient.
E Statements (1) and (2) TOGETHER are NOT sufficient.

q.) 8x(y^3) + 8 (x^3)y = [2(x^2)(y^2)] / [2^(-3)]

What is xy?

(1) y>x
(2) x<0

(A) Statement (1) alone is sufficient, but statement (2) alone is not sufficient.
(B) Statement (2) alone is sufficient, but statement (1) alone is not sufficient.
(C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
(D) Each statement ALONE is sufficient.
(E) Statements (1) and (2) TOGETHER are NOT sufficient.
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Re: DS problems

by jayhawk2001 » Wed Apr 18, 2007 9:34 pm
Gabriel, I had a good mental workout :-). I seriously hope such
questions won't show up on GMAT or show up as experimental
questions.
gabriel wrote:guys here are some good DS problems ... try and solve them ..

q.) Train A leaves New York for Boston at 3 PM and travels at the constant speed of 100 mph. An hour later, it passes Train B, which is making the trip from Boston to New York at a constant speed. If Train B left Boston at 3:50 PM and if the combined travel time of the two trains is 2 hours, what time did Train B arrive in New York?
(1) Train B arrived in New York before Train A arrived in Boston.

(2) The distance between New York and Boston is greater than 140 miles.
I think it should be D.

The question stem can be translated into equations of the form below --

x = distance between NY and BOS
B = speed of train B

We know x/100 + x/B = 2
and 100 + B/6 = x (for train B to reach NY, it has to travel x distance)

Using 2 in 1, we get

B^2 - 500B + 60000 = 0
B = 200 or 300
Correspondingly x = 150 or 800/6

1 tells us that B arrived before A. Only B=300 satisfies this.
If we choose B=200, A will arrive at 4:20 and B will arrive at 4:30
If we choose B=300, A will arrive at 4:30 and B will arrive at 4:20


2 tells us that x > 140 which implies it has to be 150 and hence
sufficient.

gabriel wrote: q.)Last Friday a certain shop sold 3/4 of the sweaters in its inventory. Each sweater sold or $20. What was the total revenue last Friday from the sale of these sweaters?

(1) When the shop opened last Friday, there were 160 sweaters in its inventory.
(2) All but 40 sweaters in the shop’s inventory were sold last Friday.
1 - sufficient. 3/4 * 160 * 20 is the revenue
2 - sufficient. 1/4 of inv = 40, so 3/4 = 120. So revenue = 120 * 20

Hence D

gabriel wrote:
q.) 8x(y^3) + 8 (x^3)y = [2(x^2)(y^2)] / [2^(-3)]

What is xy?

(1) y>x
(2) x<0
We can translate the equation to

8xy (x^2 + y^2) = 8xy(2xy)
8xy*(x-y)^2 = 0

So, xy = 0 or (x-y)^2 = 0

1 - sufficient. x-y cannot be zero. So xy = 0

2 - insufficient. If x = y, then xy need not be zero. If x != y, then xy = 0

So, I think it should be A
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by Prasanna » Fri Apr 20, 2007 6:05 am
Hi

I am unable to understand the second equation you had derived in the first problem.

"and 100 + B/6 = x (for train B to reach NY, it has to travel x distance)"

Request you to help.

Prasanna
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by jayhawk2001 » Fri Apr 20, 2007 5:45 pm
Prasanna wrote:Hi

I am unable to understand the second equation you had derived in the first problem.

"and 100 + B/6 = x (for train B to reach NY, it has to travel x distance)"

Request you to help.

Prasanna
x is the total distance between NY and BOS. We know the 2 trains meet
at a point which is 100 miles from NY.

We also know that B * 10min/60min is the total distance that B would have
traveled from BOS to the point in between.

So, 100 + B/6 = x
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Re: DS problems

by gabriel » Sat Apr 21, 2007 1:14 am
jayhawk2001 wrote:Gabriel, I had a good mental workout :-). I seriously hope such
questions won't show up on GMAT or show up as experimental
questions.
gabriel wrote:guys here are some good DS problems ... try and solve them ..

q.) Train A leaves New York for Boston at 3 PM and travels at the constant speed of 100 mph. An hour later, it passes Train B, which is making the trip from Boston to New York at a constant speed. If Train B left Boston at 3:50 PM and if the combined travel time of the two trains is 2 hours, what time did Train B arrive in New York?
(1) Train B arrived in New York before Train A arrived in Boston.

(2) The distance between New York and Boston is greater than 140 miles.
I think it should be D.

The question stem can be translated into equations of the form below --

x = distance between NY and BOS
B = speed of train B

We know x/100 + x/B = 2
and 100 + B/6 = x (for train B to reach NY, it has to travel x distance)

Using 2 in 1, we get

B^2 - 500B + 60000 = 0
B = 200 or 300
Correspondingly x = 150 or 800/6

1 tells us that B arrived before A. Only B=300 satisfies this.
If we choose B=200, A will arrive at 4:20 and B will arrive at 4:30
If we choose B=300, A will arrive at 4:30 and B will arrive at 4:20


2 tells us that x > 140 which implies it has to be 150 and hence
sufficient.

gabriel wrote: q.)Last Friday a certain shop sold 3/4 of the sweaters in its inventory. Each sweater sold or $20. What was the total revenue last Friday from the sale of these sweaters?

(1) When the shop opened last Friday, there were 160 sweaters in its inventory.
(2) All but 40 sweaters in the shop’s inventory were sold last Friday.
1 - sufficient. 3/4 * 160 * 20 is the revenue
2 - sufficient. 1/4 of inv = 40, so 3/4 = 120. So revenue = 120 * 20

Hence D

gabriel wrote:
q.) 8x(y^3) + 8 (x^3)y = [2(x^2)(y^2)] / [2^(-3)]

What is xy?

(1) y>x
(2) x<0
We can translate the equation to

8xy (x^2 + y^2) = 8xy(2xy)
8xy*(x-y)^2 = 0

So, xy = 0 or (x-y)^2 = 0

1 - sufficient. x-y cannot be zero. So xy = 0

2 - insufficient. If x = y, then xy need not be zero. If x != y, then xy = 0

So, I think it should be A

excellent dood :D .... u got all of them right ... seems like u ready to take the gmat on (head on) ... these were q's that i got form some other forums ( no copyright issues :D ) ... and they are defnitely in the range of 730 -760 ( i just loved the first q) .. so i dont think u shuld be really worried abt the quant part anymore ..
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by f2001290 » Sat Apr 21, 2007 2:48 am
1st and 3rd questions have broken my confidence.

Gabriel - what is the beat strategy to solve these sort of questions?
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by Prasanna » Sat Apr 21, 2007 4:19 pm
Thanks...How stupid I was
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