Data Sufficiency Questions

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Data Sufficiency Questions

by Anamaiy » Sat Apr 16, 2011 12:58 am
Hi guys,

need help with these problems:

A). Each employee in a task force is either a manager or a director. What percentage of the task force are directors?
1). The avg. salary of managers on task force is 5000$ less than avg. salary of all employees on task force.
2). The avg. salary of directors on task force is 15000$ more than avg. salary of all employees on task force.


B). Did it take Pei more than 2 hrs to walk 10 miles?(1mile = 1.6 km approx).
1). Pei walked at an avg. speed of less than 6.4 kmph.
2). On avg., it took Pei more than 9 min per kilometer to walk this distance.


C). Is m+z>0?
1). m-3z>0.
2). 4z-m>0.


D). A manufacture conducted a survey to determine how many people buy products P and Q. What fraction of the people said that they bought neither P nor Q?
1). 1/3 of the people surveyed said they bought P but not Q.
2). 1/2 of the people surveyed said they bought Q.


E). If x,y and z are integers greater than 1, what is the value of x+y+z?
1). xyz = 70
2). x/yz = 7/10

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by maihuna » Sat Apr 16, 2011 1:55 am
B). Did it take Pei more than 2 hrs to walk 10 miles?(1mile = 1.6 km approx).
1). Pei walked at an avg. speed of less than 6.4 kmph.
2). On avg., it took Pei more than 9 min per kilometer to walk this distance.

1 at 6.4kmph it requires 10*1.6/6.4 = 2.5 so time is going to be more than 2.5 hrs and so A is suff

2. 9 min pkm req 10*1.6*9/60 = .8*3 = 2.4 hrs so time req is more than 2.4 and so B is suff

ANs D
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by Anurag@Gurome » Sat Apr 16, 2011 2:01 am
Q1. Each employee in a task force is either a manager or a director. What percentage of the task force are directors?
1). The avg. salary of managers on task force is 5000$ less than avg. salary of all employees on task force.
2). The avg. salary of directors on task force is 15000$ more than avg. salary of all employees on task force.

Explanation:
Let us assume the following:
No. of managers = m
No. of directors = d
Avg. salary of all employees on task force = x

(1) The avg. salary of managers on task force = x - 5000. But this info ALONE is NOT SUFFICIENT.

(2) The avg. salary of directors on task force = x + 15000. Again this info ALONE is NOT SUFFICIENT.

Combining (1) and (2), Sum of the salaries of managers and directors = m(x - 5000) + d(x + 15000), which will also be equal to (m + d)x.
So, m(x - 5000) + d(x + 15000) = (m + d)x
5000m = 15000d
m = 3d or m:d = 3:1, which means we can find the percentage of task force who are directors.
Hence, combining is SUFFICIENT to answer the question.

The correct answer is C.
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by Anurag@Gurome » Sat Apr 16, 2011 2:06 am
Q3. Is m+z>0?
1). m-3z>0.
2). 4z-m>0.

Explanation:

(1) m - 3z > 0 implies m > 3z. But this is NOT SUFFICIENT to say whether m + z > 0.

(2) 4z - m > 0 implies m < 4z. Again this is NOT SUFFICIENT to say whether m + z > 0.

Combining (1) and (2), add both the inequalities, z > 0
Since m > 3z so m is also > 0
Therefore, m + z > 0.
SUFFICIENT.

The correct answer is C.
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by Anurag@Gurome » Sat Apr 16, 2011 2:20 am
Q4. A manufacture conducted a survey to determine how many people buy products P and Q. What fraction of the people said that they bought neither P nor Q?
1) 1/3 of the people surveyed said they bought P but not Q.
2) 1/2 of the people surveyed said they bought Q.

Explanation:

Let the total people surveyed = x.

See the Venn Diagram below:

Image

(1) ALONE is NOT SUFFICIENT.
(2) ALONE is NOT SUFFICIENT.

Combining (1) and (2), (Neither P nor Q) + x/3 + x/2 = x
So, Neither P nor Q = x - 5x/6 = x/6
So, 1/6th of the people neither bought P nor Q.

The correct answer is C.
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by Anurag@Gurome » Sat Apr 16, 2011 2:37 am
Q5. If x,y and z are integers greater than 1, what is the value of x+y+z?
1) xyz = 70
2) x/yz = 7/10

Explanation:

(1) xyz = 70
Prime factors of 70 = 2 * 5 * 7 implies x + y + z = 14
2, 5, and 7 can be the only values of x, y, z because if you try any other combination that will not suffice the given condition of x, y, z > 1.
(if we take x = 1, y = 14, z = 5, here x = 1 does not satisfy the given condition)
So, (1) is SUFFICIENT.

(2) x/yz = 7/10 or 2 * 5 * x = 7 * y * z
If x = 14, y = 2, z = 10, then x + y + z = 26
If x = 28, y = 10, z = 4, then x + y + z = 42
No unique answer.
So, (2) is NOT SUFFICIENT.

The correct answer is A.
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