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
Data Sufficiency Questions
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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
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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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.
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.
Anurag Mairal, Ph.D., MBA
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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.
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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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:
(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.
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:
(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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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.
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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