quants problems

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nagar.sandeep: Junior | Next Rank: 30 Posts; Posts: 13; Joined: Sun Jul 25, 2010 8:37 am

by nagar.sandeep » Fri Sep 10, 2010 10:24 pm

Hi,

It will be nice if anyone could help me with couple of quants problems, which are listed down:

Q1 What is the median number of employees assigned per project for the projects at Company Z?
(1) 25 percent of the projects at Company Z have 4 or more employees assigned to each
project.
(2) 35 percent of the projects at Company Z have 2 or fewer employees assigned to each
project.

Q2 For any positive integer x, the 2-height of x is defined to be the greatest nonnegative
integer n such that 2n is a factor of x. If k and m are positive integers, is the 2-height of k
greater than the 2-height of m ?
(1) k > m
(2)k/m is an even integer

Q3 In the decimal representation of x, where 0 < x < 1, is the tenths digit of x nonzero?
(1) 16x is an integer.
(2) 8x is an integer.

Any help will be appreciated.

Thanks,
Sandeep

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Source: Beat The GMAT — Problem Solving | Fri Sep 10, 2010 10:24 pm

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Rahul@gurome: GMAT Instructor; Posts: 1179; Joined: Sun Apr 11, 2010 9:07 pmFollowed by: 88 members; Location: Milpitas, CA; Thanked: 447 times

by Rahul@gurome » Fri Sep 10, 2010 11:53 pm

Q1. What is the median number of employees assigned per project for the projects at Company Z?
(1) 25 percent of the projects at Company Z have 4 or more employees assigned to each project.
(2) 35 percent of the projects at Company Z have 2 or fewer employees assigned to each project.

Explanation:

(1) Median is the value that separates the upper and lower half of the sample. (1) gives that 25% of projects have 4 or more employees to each project . But the % of projects that have less than 4 employees is not given. So, (1) is NOT SUFFICIENT.

(2) From this statement, the % of projects that have more than 2 employees is not given. As above, (2) is also NOT SUFFICIENT.

Combining (1) and (2), 35% projects have 2 or fewer employees, 25% of the projects have 4 or more employees, so the remaining % of projects = 100 - (35 + 25) = 40% projects should have exactly 3 employees (between 2 and 4).
Therefore, median number of employees assigned per project = 3

The correct answer is [spoiler](C)[/spoiler].

Rahul Lakhani
Quant Expert
Gurome, Inc.
https://www.GuroMe.com
On MBA sabbatical (at ISB) for 2011-12 - will stay active as time permits
1-800-566-4043 (USA)
+91-99201 32411 (India)

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Rahul@gurome: GMAT Instructor; Posts: 1179; Joined: Sun Apr 11, 2010 9:07 pmFollowed by: 88 members; Location: Milpitas, CA; Thanked: 447 times

by Rahul@gurome » Sat Sep 11, 2010 12:18 am

Q2. For any positive integer x, the 2-height of x is defined to be the greatest nonnegative
integer n such that 2n is a factor of x. If k and m are positive integers, is the 2-height of k
greater than the 2-height of m?
(1) k > m
(2)k/m is an even integer

Explanation:

(1) k > m does not imply that the 2-height (that is the number of 2's in the prime factorization of an integer) of k is greater than the 2-height of m. It may or may not be greater than the 2-height of m.
If k = 22 and m = 12, then 2-height of k is less than 2-height of m.
If k = 12 and m = 10, then 2-height of k is greater than 2-height of m.
No unique answer.
So, (1) is NOT SUFFICIENT.

(2) k/m can be an even integer if k's 2-height is greater than the m's 2-height.
If k = 14 and m = 7, then k's 2-height is greater than the m's 2-height.
If k = 12 and m = 6, then k's 2-height is greater than the m's 2-height.
So, (2) is SUFFICIENT.

The correct answer is [spoiler](B)[/spoiler].

Rahul Lakhani
Quant Expert
Gurome, Inc.
https://www.GuroMe.com
On MBA sabbatical (at ISB) for 2011-12 - will stay active as time permits
1-800-566-4043 (USA)
+91-99201 32411 (India)

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Rahul@gurome: GMAT Instructor; Posts: 1179; Joined: Sun Apr 11, 2010 9:07 pmFollowed by: 88 members; Location: Milpitas, CA; Thanked: 447 times

by Rahul@gurome » Sat Sep 11, 2010 12:25 am

Q3. In the decimal representation of x, where 0 < x < 1, is the tenths digit of x nonzero?
(1) 16x is an integer.
(2) 8x is an integer.

Explanation:

(1) If x = 1/2 = 0.5, then tenths digit of x = 5
If x = 1/16 = 0.0625, then tenths digit of x = 0
So, the tenths digit of x may or may not be zero. No unique answer.
So, (1) is NOT SUFFICIENT.

(2) If x = 1/2 = 0.5, then tenths digit of x = 5, which is non-zero.
If x = 1/8 = 0.125, then tenths digit of x = 1, which is non-zero. This implies that all numbers in the tenth place between 0 < x < 1 will always have a non-zero integer.
So, (2) is SUFFICIENT.

The correct answer is [spoiler](B)[/spoiler].

Rahul Lakhani
Quant Expert
Gurome, Inc.
https://www.GuroMe.com
On MBA sabbatical (at ISB) for 2011-12 - will stay active as time permits
1-800-566-4043 (USA)
+91-99201 32411 (India)

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Crystal W: Master | Next Rank: 500 Posts; Posts: 154; Joined: Wed Mar 02, 2016 9:34 am; Thanked: 2 times

by Crystal W » Thu Apr 14, 2016 6:01 am

Rahul@gurome wrote:Q2. For any positive integer x, the 2-height of x is defined to be the greatest nonnegative
integer n such that 2n is a factor of x. If k and m are positive integers, is the 2-height of k
greater than the 2-height of m?
(1) k > m
(2)k/m is an even integer

Explanation:

(1) k > m does not imply that the 2-height (that is the number of 2's in the prime factorization of an integer) of k is greater than the 2-height of m. It may or may not be greater than the 2-height of m.
If k = 22 and m = 12, then 2-height of k is less than 2-height of m.
If k = 12 and m = 10, then 2-height of k is greater than 2-height of m.
No unique answer.
So, (1) is NOT SUFFICIENT.

(2) k/m can be an even integer if k's 2-height is greater than the m's 2-height.
If k = 14 and m = 7, then k's 2-height is greater than the m's 2-height.
If k = 12 and m = 6, then k's 2-height is greater than the m's 2-height.
So, (2) is SUFFICIENT.

The correct answer is [spoiler](B)[/spoiler].

Thank you for your explanation! Can you explain more about what is the meaning of the question?

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[email protected]: Elite Legendary Member; Posts: 10392; Joined: Sun Jun 23, 2013 6:38 pmFollowed by: 511 members; Location: Palo Alto, CA; Thanked: 2867 times; GMAT Score:800

by [email protected] » Thu Apr 14, 2016 9:43 am

Hi Crystal W,

The prior posts are all over 5 years old, so it's likely that the original posters are long gone. What specifically would you like to know about this prompt?

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]

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Crystal W: Master | Next Rank: 500 Posts; Posts: 154; Joined: Wed Mar 02, 2016 9:34 am; Thanked: 2 times

by Crystal W » Thu Apr 14, 2016 1:58 pm

[email protected] wrote:Hi Crystal W,

The prior posts are all over 5 years old, so it's likely that the original posters are long gone. What specifically would you like to know about this prompt?

GMAT assassins aren't born, they're made,
Rich

I cannot understand the question meaning. The description makes me so confused. Can you explain it?

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OptimusPrep: Master | Next Rank: 500 Posts; Posts: 410; Joined: Fri Mar 13, 2015 3:36 amFollowed by: 8 members; Location: Worldwide; Thanked: 120 times; GMAT Score:770

by OptimusPrep » Thu Apr 14, 2016 6:44 pm

Crystal W wrote: Thank you for your explanation! Can you explain more about what is the meaning of the question?

Hi Crystal W,

First things first, i think there is a problem with the question. The question should read "For any positive integer x, the 2-height of x is defined to be the greatest non-negative integer n such that 2^n is a factor of x"

Now let us talk about 2-height of a number.
Assume x = 20 = 2^2*5
Here 2-height of 20 = 2, since the highest power of 2 is 2
Assume x = 10 = 2^1*5
Here 2-height of 10 = 1, since the highest power of 2 is 1

You simply need to find out the powers of two in the prime factorization.
Does this help?

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Matt@VeritasPrep: GMAT Instructor; Posts: 2630; Joined: Wed Sep 12, 2012 3:32 pmFollowed by: 119 members; Location: East Bay all the way; Thanked: 625 times; GMAT Score:780

by Matt@VeritasPrep » Fri Apr 15, 2016 12:49 pm

Crystal W wrote:
[email protected] wrote:Hi Crystal W,

The prior posts are all over 5 years old, so it's likely that the original posters are long gone. What specifically would you like to know about this prompt?

GMAT assassins aren't born, they're made,
Rich
I cannot understand the question meaning. The description makes me so confused. Can you explain it?

It's essentially asking how many times you can divide x by 2 and still have an integer.

For example, take the number 24.

24/2 = 12
12/2 = 6
6/2 = 3

So we can divide 24 by 2 THREE TIMES and still have an integer. (If we kept going, 3/2 wouldn't be, so we have to stop at this point.) So the 2-height of 24 is 3.

Save $100 on any VP online course!

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Crystal W: Master | Next Rank: 500 Posts; Posts: 154; Joined: Wed Mar 02, 2016 9:34 am; Thanked: 2 times

by Crystal W » Fri Apr 15, 2016 2:16 pm

OptimusPrep wrote:
Crystal W wrote: Thank you for your explanation! Can you explain more about what is the meaning of the question?
Hi Crystal W,

First things first, i think there is a problem with the question. The question should read "For any positive integer x, the 2-height of x is defined to be the greatest non-negative integer n such that 2^n is a factor of x"

Now let us talk about 2-height of a number.
Assume x = 20 = 2^2*5
Here 2-height of 20 = 2, since the highest power of 2 is 2
Assume x = 10 = 2^1*5
Here 2-height of 10 = 1, since the highest power of 2 is 1

You simply need to find out the powers of two in the prime factorization.
Does this help?

It is really helpful! Thank you so much!

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Crystal W: Master | Next Rank: 500 Posts; Posts: 154; Joined: Wed Mar 02, 2016 9:34 am; Thanked: 2 times

by Crystal W » Fri Apr 15, 2016 2:18 pm

Matt@VeritasPrep wrote:
Crystal W wrote:
[email protected] wrote:Hi Crystal W,

The prior posts are all over 5 years old, so it's likely that the original posters are long gone. What specifically would you like to know about this prompt?

GMAT assassins aren't born, they're made,
Rich
I cannot understand the question meaning. The description makes me so confused. Can you explain it?
It's essentially asking how many times you can divide x by 2 and still have an integer.

For example, take the number 24.

24/2 = 12
12/2 = 6
6/2 = 3

So we can divide 24 by 2 THREE TIMES and still have an integer. (If we kept going, 3/2 wouldn't be, so we have to stop at this point.) So the 2-height of 24 is 3.

Thank you for your help! Hoewever, I believe in OG 2016, it's 2^n instead 2n

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