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3 Quant questions - kindly back to me with the solution

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3 Quant questions - kindly back to me with the solution

by roopa ramesh » Sun Sep 28, 2014 9:49 am
Dear All,



I need help on the foll 3 questions - as I have not been able to solve them.


** for the figures, pl. do refer to the attachment.




In the figure shown above, point O is the centre of the circle and points B, C, D lie on the semi-cricle. If the length of the line segment AB is equal to the line segment OC, what is the measure of BAO?
1) Angle: COD: is 60
2) Angle BCO is: 40
Answer is: D

_________________________________________
During a 40-mile trip, Marla travelled at an average speed of "x" miles per hour for the first "y" miles of the trip and then at an avg speed of 1.25x MPH for the last 40-y miles of the trip. The time that Marla took to travel 40 miles was what percent of the time it wud have taken her if she dhad travlled at: x MPH for the entire trip?
x=48
y=20
Ans: B
__________________________________________
If p and n are +ve integers and p>n, then what is the remiander when p^2- n^2 is divided by 15?
1. The remainder when p+n is divided by 5 is 1.
2. The remidner when p-n is divided by 3 is 1.
Ans: E


Kindly write back to me at the earliest as I ahve my GMAT exam on: 10th Oct'14.


reg

roopa
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For figures - see the attached file
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by GMATGuruNY » Sun Sep 28, 2014 10:04 am
roopa ramesh wrote: In the figure shown above, point O is the centre of the circle and points B, C, D lie on the semi-cricle. If the length of the line segment AB is equal to the line segment OC, what is the measure of BAO?
1) Angle: COD: is 60
2) Angle BCO is: 40
I posted a solution here:

https://www.beatthegmat.com/geometry-ds- ... 17171.html
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by [email protected] » Sun Sep 28, 2014 10:41 am
Hi roopa ramesh,

Here are some suggestions about posting questions in these Forums:

1) Please post the questions in the proper Forum. These are DS questions; they should be posted in the DS Forum.
2) Please post just 1 question per thread. With 3 questions, you could have 3 different discussions with 3 different sets of folio-up questions. To avoid confusion, it's best to post each question individually.

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by GMATGuruNY » Mon Sep 29, 2014 3:03 am
roopa ramesh wrote: During a 40-mile trip, Marla travelled at an average speed of "x" miles per hour for the first "y" miles of the trip and then at an avg speed of 1.25x MPH for the last 40-y miles of the trip. The time that Marla took to travel 40 miles was what percent of the time it wud have taken her if she dhad travlled at: x MPH for the entire trip?
x=48
y=20
Statement 1: x = 48, implying that the rate for the last 40-y miles = (5/4) * 48 = 60 miles per hour.
Time for the entire trip at x=48 miles per hour:
d/r = 40/48 = 5/6 hour.

Case 1: y=20
Time for the first 20 miles = d/r = 20/48 = 5/12 hour.
Time for the last 20 miles = d/r = 20/60 = 4/12 hour.
Total time = 5/12 + 4/12 = 9/12 hour.
Resulting ratio:
(shorter time)/(longer time) = (9/12) / (5/6) = 9/10.

Case 2: y=10
Time for the first 10 miles = d/r = 10/48 = 5/24 hour.
Time for the last 30 miles = d/r = 30/60 = 1/2 hour.
Total time = 5/24 + 1/2 = 17/24 hours.
Resulting ratio:
(shorter time)/(longer time) = (17/24) / (5/6) = 17/20.

Since different ratios are possible, INSUFFICIENT.

Statement 2: y = 20
Case 1 also satisfies statement 2.

Case 3: x=4 miles per hour, 1.25x = 5 miles per hour
Time for the first 20 miles = d/r = 20/4 = 5 hours.
Time for the last 20 miles = d/r = 20/5 = 4 hours.
Total time = 5+4 = 9 hours.
Time for the entire trip at x=4 miles per hour:
d/r = 40/4 = 10 hours.
Resulting ratio:
(shorter time)/(longer time) = 9/10.

Case 1 and Case 3 illustrate that -- if y=20 -- then the resulting ratio will always be the SAME:
(shorter time)/(longer time) = 9/10.
SUFFICIENT.

The correct answer is B.
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by GMATGuruNY » Mon Sep 29, 2014 3:05 am
roopa ramesh wrote: If p and n are +ve integers and p>n, then what is the remiander when p^2- n^2 is divided by 15?
1. The remainder when p+n is divided by 5 is 1.
2. The remidner when p-n is divided by 3 is 1.
Statement 1:
In other words, p+n a (MULTIPLE OF 5) + 1.
Thus:
p+n = 5a + 1 = 1, 6, 11, 16, 21...

Let p+n = 6.
If p=5 and n=1, then p²-n² = 24, in which case dividing by 15 will yield a remainder of 9.
If p=4 and n=2, then p²-n² = 12, in which case dividing by 15 will yield a remainder of 12.
Since the remainder can be different values, INSUFFICIENT.

Statement 2:
In other words, p-n is a (MULTIPLE OF 3) + 1.
Thus:
p-n = 3b + 1 = 1, 4, 7, 10, 13, 16...

Let p-n= 4.
If p=5 and n=1, then p²-n² = 24, in which case dividing by 15 will yield a remainder of 9.
If p=6 and n=2, then p²-n² = 32, in which case dividing by 15 will yield a remainder of 2.
Since the remainder can be different values, INSUFFICIENT.

Statements combined:
Statement 1: p+n = 1, 6, 11, 16, 21...
Statement 2: p-n = 1, 4, 7, 10, 13, 16...

If p+n=6 and p-n=4, then p=5 and n=1.
Here, p²-n² = 24, in which case dividing by 15 will yield a remainder of 9.
If p+n=11 and p-n=1, then p=6 and n=5.
Here, p²-n² = 11, in which case dividing by 15 will yield a remainder of 11.
Since the remainder can be different values, INSUFFICIENT.

The correct answer is E.
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by pooja181 » Tue Sep 30, 2014 4:28 am
Statement 1: x = 48, implying that the rate for the last 40-y miles = (5/4) * 48 = 60 miles per hour.
Time for the entire trip at x=48 miles per hour:
d/r = 40/48 = 5/6 hour.

Case 1: y=20
Time for the first 20 miles = d/r = 20/48 = 5/12 hour.
Time for the last 20 miles = d/r = 20/60 = 4/12 hour.
Total time = 5/12 + 4/12 = 9/12 hour.
Resulting ratio:
(shorter time)/(longer time) = (9/12) / (5/6) = 9/10.

Case 2: y=10
Time for the first 10 miles = d/r = 10/48 = 5/24 hour.
Time for the last 30 miles = d/r = 30/60 = 1/2 hour.
Total time = 5/24 + 1/2 = 17/24 hours.
Resulting ratio:
(shorter time)/(longer time) = (17/24) / (5/6) = 17/20.

Since different ratios are possible, INSUFFICIENT.

Statement 2: y = 20
Case 1 also satisfies statement 2.

Case 3: x=4 miles per hour, 1.25x = 5 miles per hour
Time for the first 20 miles = d/r = 20/4 = 5 hours.
Time for the last 20 miles = d/r = 20/5 = 4 hours.
Total time = 5+4 = 9 hours.
Time for the entire trip at x=4 miles per hour:
d/r = 40/4 = 10 hours.
Resulting ratio:
(shorter time)/(longer time) = 9/10.

Case 1 and Case 3 illustrate that -- if y=20 -- then the resulting ratio will always be the SAME:
(shorter time)/(longer time) = 9/10.
SUFFICIENT.

The correct answer is B.


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by Brent@GMATPrepNow » Tue Sep 30, 2014 6:57 am
If p and n are positive integers and p > n, what is the remainder when p² - n² is divided by 15?
(1) The remainder when (p + n) is divided by 5 is 1.
(2) The remainder when (p - n) is divided by 3 is 1.
Target question: What is the remainder when p² - n² is divided by 15

NOTE that p² - n² is a difference of squares, so we can FACTOR it to get: p² - n² = (p + n)(p - n). Since both (p + n) and (p - n) are in the statements, it may be useful to REPHRASE the target question...

REPHRASED target question: What is the remainder when (p + n)(p - n) is divided by 15?

Statement 1: The remainder when (p + n) is divided by 5 is 1
This tell us that (p + n) is NOT DIVISIBLE by 5.
Since there's no information about (p-n), we can't determine the remainder when (p + n)(p - n) is divided by 15
Consider these two conflicting cases:
Case a: p = 5 and n = 1 (notice that the remainder when p+n is divided by 5 is 1). In this case, the remainder when is 9 when (p + n)(p - n) is divided by 15
Case b: p = 1 and n = 0 (notice that the remainder when p+n is divided by 5 is 1). In this case, the remainder when is 1 when (p + n)(p - n) is divided by 15
So, 2 of the numbers are less than 30
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: The remainder when p - n is divided by 3 is 1
Here we have no information about p+n.
Consider these two conflicting cases:
Case a: p = 5 and n = 1 (notice that the remainder when p-n is divided by 3 is 1). In this case, the remainder when is 9 when (p + n)(p - n) is divided by 15
Case b: p = 1 and n = 0 (notice that the remainder when p-n is divided by 3 is 1). In this case, the remainder when is 1 when (p + n)(p - n) is divided by 15
So, 2 of the numbers are less than 30
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
IMPORTANT: Notice that I happened to use the same values for the counter-examples in each statement. This means that we can use the same values here to show that the COMBINED statements are not sufficient. That is...
Consider these two conflicting cases:
Case a: p = 5 and n = 1 (notice that both statements are satisfied). In this case, the remainder when is 9 when (p + n)(p - n) is divided by 15
Case b: p = 1 and n = 0 (notice that both statements are satisfied). In this case, the remainder when is 1 when (p + n)(p - n) is divided by 15
So, 2 of the numbers are less than 30
Since we cannot answer the target question with certainty, the COMBINED statements are NOT SUFFICIENT

Answer: E

ALTERNATIVELY, when examining the statements combined, we can use a nice rule that says:
If N divided by D, leaves remainder R, then the possible values of N are R, R+D, R+2D, R+3D,. . . etc.
For example, if k divided by 5 leaves a remainder of 1, then the possible values of k are: 1, 1+5, 1+(2)(5), 1+(3)(5), 1+(4)(5), . . . etc.

Okay, onto the question . . .
Statement 1: Applying the above rule, some possible values of p+n are 6, 11, 16, 21, 26, etc.
Aside: you'll notice that I didn't include 1 as a possible value since we're told that p and n are positive integers, and we can't get a sum of 1 if both are positive

Statement 2: Applying the above rule, some possible values of p-n are 1, 4, 7, 10, 13, etc

Let's examine two cases with conflicting results.

case a: p+n = 11 and p-n = 1
Add the equations to get 2p = 12, which means p = 6 and n = 5 (perfect, we have positive integer values for p and n)
In this case, when (p + n)(p - n) is divided by 15, the remainder is 11

case b: p+n = 6 and p-n = 4
Add the equations to get 2p = 10, which means p = 5 and n = 1 (perfect, we have positive integer values for p and n)
In this case, when (p + n)(p - n) is divided by 15, the remainder is 9
Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Answer = E

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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