Quantitative
Aptitude Data Sufficiency Practice Set – 4
Directions (1 – 14): Given below is a question and some
statements given below it. You have to decide whether the data provided in the
statements is sufficient to answer the question. You should use the given data
and your knowledge of Mathematics to choose between the possible answers.
1. What is the length of line segment PQ?
I. Triangle PQR is right angled.
II. Length of QR is half the length of
PR.
(a) The data in statement I alone is
sufficient to answer the question, while the data in statement II alone is not
sufficient to answer the question.
(b) The data in statement II alone is
sufficient to answer the question, while the data in statement I alone is not
sufficient to answer the question.
(c) The data in statement I alone or in
statement II alone is sufficient to answer the question.
(d) The data in both the statements I and
II is not sufficient to answer the question.
(e) The data in both the statements I and
II together is necessary to answer the question.
2. In how many days can B alone finish the work?
I. A, B and C together can finish the
work in 3 days.
II. B and C together can finish the work
in 5 days.
(a) The data in statement I alone is
sufficient to answer the question, while the data in statement II alone is not
sufficient to answer the question.
(b) The data in statement II alone is
sufficient to answer the question, while the data in statement I alone is not
sufficient to answer the question.
(c) The data in statement I alone or in
statement II alone is sufficient to answer the question.
(d) The data in both the statements I and
II is not sufficient to answer the question.
(e) The data in both the statements I and
II together is necessary to answer the question.
3. What will the LCM of natural numbers M, N and
P(in terms of M, N and P)?
I. M is a multiple of N.
II. M and P are relatively prime.
(a) The data in statement I alone is
sufficient to answer the question, while the data in statement II alone is not
sufficient to answer the question.
(b) The data in statement II alone is
sufficient to answer the question, while the data in statement I alone is not
sufficient to answer the question.
(c) The data in statement I alone or in
statement II alone is sufficient to answer the question.
(d) The data in both the statements I and
II is not sufficient to answer the question.
(e) The data in both the statements I and
II together is necessary to answer the question.
4. How many mangoes Shane has?
I. Shane and Mark have a total of 103
mangoes.
II. The number of mangoes with both
Shane and Mark are prime.
(a) The data in statement I alone is
sufficient to answer the question, while the data in statement II alone is not
sufficient to answer the question.
(b) The data in statement II alone is
sufficient to answer the question, while the data in statement I alone is not
sufficient to answer the question.
(c) The data in statement I alone or in
statement II alone is sufficient to answer the question.
(d) The data in both the statements I and
II is not sufficient to answer the question.
(e) The data in both the statements I and
II together is necessary to answer the question.
5. What will be the value of P, where P = (M  N)^{(M
+ N)}?
I. N is a multiple of 10.
II. M is a multiple of 5.
(a) The data in statement I alone is
sufficient to answer the question, while the data in statement II alone is not
sufficient to answer the question.
(b) The data in statement II alone is
sufficient to answer the question, while the data in statement I alone is not
sufficient to answer the question.
(c) The data in statement I alone or in
statement II alone is sufficient to answer the question.
(d) The data in both the statements I and
II is not sufficient to answer the question.
(e) The data in both the statements I and
II together is necessary to answer the question.
6. From a pack of 52 cards, N kings are removed.
What is the value of N?
I. The probability of getting a king
when a card is randomly drawn is 1/25.
II. The probability of getting a queen
when a card is randomly drawn is 2/25.
(a) The data in statement I alone is
sufficient to answer the question, while the data in statement II alone is not
sufficient to answer the question.
(b) The data in statement II alone is
sufficient to answer the question, while the data in statement I alone is not
sufficient to answer the question.
(c) The data in statement I alone or in
statement II alone is sufficient to answer the question.
(d) The data in both the statements I and
II is not sufficient to answer the question.
(e) The data in both the statements I and
II together is necessary to answer the question.
7. When one ball is drawn at random form a bag
containing 30 balls, what is the chance that it is pink?
I. The bag contains 10 yellow and 8 green
balls.
II. The bag contains all coloured balls.
(a) The statement I alone is sufficient
to answer the question but the statement II alone is not sufficient
(b) The statement II alone is sufficient
to answer the question but the statement I alone is not sufficient
(c) Both statements I and II together are
needed to answer the question
(d) Either to statement I alone or
statement II alone is sufficient to answer the question
(e) You cannot get the answer from the
statement I and II together but need even more data
8. Abhimanyu took a loan of some amount from a
bank. What is his rate of interest per annum if
I. The amount becomes Rs. 11025 at
compound interest after 2 yr
II. The same amount with
simple interest becomes Rs. 11000 after two years
III. The amount invested is
Rs. 10000.
(a) Only I or II or III
(b) Only I or III
(c) Only II and III
(d) Only I or II
(e) All, I, II and III are required to
answer the question.
9. What is the profit of Rahul who sold two
similar bags?
I. He sold one bag at 20% loss.
II. He sold the other bag at 25% gain.
III. He has bought the two
bags at Rs.2760.
(a) Only I and II together are sufficient
(b) Only II and III together are
sufficient
(c) Any two of the three are sufficient
(d) All three together are needed
(e) All even together are not sufficient
10. A sum
of Rs. 38,500 was divided among P, Q and R. Who received the minimum amount?
I. P received 2/9 of what Q and R
together received.
II. Q received 3/11 of what P and R
together received.
11. Is 100
the average (arithmetic mean) score of the SBI PO?
I. Half of the people who take
SBI PO score above 100 and half of the people score below 100.
II. The highest SBI PO score is 150 and
the lowest score is 50.
(a) The data in statement I alone is
sufficient to answer the question, while the data in statement II alone is not
sufficient to answer the question.
(b) The data in statement II alone is
sufficient to answer the question, while the data in statement I alone is not
sufficient to answer the question.
(c) The data in statement I alone or in
statement II alone is sufficient to answer the question.
(d) The data in both the statements I and
II is not sufficient to answer the question.
(e) The data in both the statements I and
II together is necessary to answer the question.
12. Members
in a club either speak Punjabi or Hindi or both. Find the number of members in
a club who speak only Punjabi.
I. There are 300 members in the club and
the number of members who speak both Punjabi and Hindi is 196.
II. The number of members who speak only
Hindi is 58.
(a) The data in statement I alone is
sufficient to answer the question, while the data in statement II alone is not
sufficient to answer the question.
(b) The data in statement II alone is
sufficient to answer the question, while the data in statement I alone is not
sufficient to answer the question.
(c) The data in statement I alone or in
statement II alone is sufficient to answer the question.
(d) The data in both the statements I and
II is not sufficient to answer the question.
(e) The data in both the statements I and
II together is necessary to answer the question.
13. A
mobile phone was initially listed at a price that would have fetched the store
a profit of 20% on the wholesale cost. What was the wholesale cost of the
Mobile phone?
I. After reducing the listed price by
10% the mobile phone was sold for a net profit of 10 dollars.
II. The mobile phone was sold for 50
dollars.
(a) The data in statement I alone is
sufficient to answer the question, while the data in statement II alone is not
sufficient to answer the question.
(b) The data in statement II alone is
sufficient to answer the question, while the data in statement I alone is not
sufficient to answer the question.
(c) The data in statement I alone or in
statement II alone is sufficient to answer the question.
(d) The data in both the statements I and
II is not sufficient to answer the question.
(e) The data in both the statements I and
II together is necessary to answer the question.
14. In a
football match, the Indian team was behind by 2 goals with 5 minutes remaining.
Did they win the match?
I. Sunil Chhetri, the Indian striker
scored 3 goals in the last 5 minutes of the match
II. Pakistan scored a total of 3 goals in
the match
(a) The data in statement I alone is
sufficient to answer the question, while the data in statement II alone is not
sufficient to answer the question.
(b) The data in statement II alone is
sufficient to answer the question, while the data in statement I alone is not
sufficient to answer the question.
(c) The data in statement I alone or in
statement II alone is sufficient to answer the question.
(d) The data in both the statements I and
II is not sufficient to answer the question.
(e) The data in both the statements I and
II together is necessary to answer the question.
Solutions:
1. D) From statement I:
Triangle PQR is right
angled. With this only, length of PQ cannot be found.
∴ Statement I alone is not sufficient to answer the question.
From statement II:
Length of QR is half the
length of PR. No data is given about PQ.
∴ Statement II alone is not sufficient to answer the question.
From statements I and
II together:
Triangle PQR is right angled.
Length of QR is half the length of PR. So, PR = 2QR.
We do not know which side
of PQR is hypotenuse, and hence cannot form an equation between three sides of
triangle.
With only one equation,
three side lengths cannot be solved.
Also, no absolute data is
given, that is insufficient to find PQ.
∴ Using even both the statements together, we cannot answer
the given question.
2. D) From
statement I:
A, B and C together can
finish the work in 3 days. With this, we cannot find in how many days B
finishes work alone, as we have 3 variables and 1 equation.
∴ Statement I alone is not sufficient to answer the question.
From statement II:
B and C together can
finish the work in 5 days. With this, we cannot find in how many days B
finishes work alone, as we have 2 variables and 1 equation.
∴ Statement II alone is not sufficient to answer the question.
From statements I and
II together:
A, B and C together can
finish the work in 3 days. B and C together can finish the work in 5 days.
Taking B and C as single unit, we can find in how many days A can finish work
alone. But the same cannot be found for B.
∴ Using even both the statements together, we cannot answer
the given question.
3. E) From
statement I:
M is a multiple of N.
Nothing about P is known. So, LCM cannot be found.
∴ Statement I alone is not sufficient to answer the question.
From statement II:
M and P are relatively
prime. Nothing about N is known. So, LCM cannot be found.
∴ Statement II alone is not sufficient to answer the question.
From statements I and
II together:
M is a multiple of N. So,
LCM of M and N will be M. And, LCM of M, N and P will be same as LCM of M and
P.
M and P are relatively
prime. So, LCM of M and P will be MP.
∴ Using both the statements together, we can answer the given
question.
4. D) From
statement I:
Shane and Mark have a
total of 103 mangoes.
With the sum, number of
mangoes with Shane cannot be found.
∴ Statement I alone is not sufficient to answer the question.
From statement II:
The number of mangoes
with both Shane and Mark are prime.
The number of mangoes
could take many values as there can be many primes.
∴ Statement II alone is not sufficient to answer the question.
From statements I and
II together:
Shane and Mark have a
total of 103 mangoes. The number of mangoes with both Shane and Mark are prime.
Since 103 is odd, it will be a sum of odd and even. Only even prime is 2. Other
will be 101. But we cannot find if Shane has 2 mangoes or 101 mangoes.
∴ Using even both the statements together, we cannot answer
the given question.
5. D) From
statement I:
To find P, exact value of
M and N should be known.
N is a multiple of 10.
With this, M and N cannot be found.
∴ Statement I alone is not sufficient to answer the question.
From statement II:
To find P, exact value of
M and N should be known.
M is a multiple of 5.
With this, M and N cannot be found.
∴ Statement II alone is not sufficient to answer the question.
From statements I and
II together:
To find P, exact value of
M and N should be known.
N is a multiple of 10. M
is a multiple of 5. With this, M and N cannot be found.
∴ Using even both the statements together, we cannot answer
the given question.
6. C) From
statement I:
The probability of
getting a king when a card is randomly drawn is 1/25.
Probability of getting a
king when a card is randomly drawn from (52  N) cards having (4  N) kings =
(4  N)/(52  N) = 1/25
⇒ We can solve for N with this equation.
∴ Statement I alone is sufficient to answer the question.
From statement II:
The probability of
getting a queen when a card is randomly drawn is 2/25.
Probability of getting a
queen when a card is randomly drawn from (52  N) cards having 4 queens =
(4)/(52  N) = 2/25
⇒ We can solve for N with this equation.
∴ Statement II alone is sufficient to answer the question.
7. E) According
to the information given in the problem, thereare 30 balls in the bag. We have
to calculate the chance that the ball drawn is pink, when one ball is drawn at
random form the bag.
From statement (1):
The bag contains 10
yellow and 8 green balls.
In this statement there
is no specific information regarding pink balls.
∴the statement I alone is not sufficient to answer the
question.
From statement (2):
The bag contains all
coloured balls.
In this statement, there
is no specific information regarding pink balls.
∴ the statement II alone is not sufficient to answer the
question.
∴You cannot get the answer from the statement I and II
together but need even more data.
8. A)
9. D) Profit
% = (SP – CP)/CP × 100
From statement I and II,
Given: One bag at 20%
loss and other at 25% gain
∵ Price of bags is not given in these statements. Therefore
until we are not aware of the cost of bags, we cannot calculate profit percent.
From II and III,
Given: one bag at 25%
gain and CP of the bags = Rs.2760
On combining these two
statements, we have information about profit on one bag and cost of the two
bags, but until we don’t know profit/loss of the second bag, we cannot reach at
the overall gain%.
From I, II and III,
Given: One bag at 20%
loss, other at 25% gain and CP of the bags = Rs.2760
Cost of one bag =
Rs.(2760/2) = Rs.1380
Now, statement I and II
will give SP of each bag and then by using the formula of profit %, we can
calculate overall profit %.
∴ all statements are necessary to reach at the solution.
10. E)
11. D) From
statement I: This statement alone does not give sufficient information
as we do not know how much above/below 100 these aspirants scored.
From statement II: Using the second statement
alone, we can't say whether 100 is the average score of SBI PO.
From I and II: Even now,
we can't determined the average.
12. E)
13. A) Let
100x be the wholesale cost of the mobile phone.
∴ List price of the mobile phone = 120x
From statement I: Selling price = 0.9 × List Price =
0.9 × 120x = 108x
Now, Profit = Selling
price – Cost price
∴ (108x) – (100x) = 10
=> x = 10/8
∴ Wholesale Cost = 100x = 125
∴ Statement I alone is sufficient.
Case II:
This gives the selling
price of the mobile phone but it is not mentioned whether any discount is
provided on the list price or not.
Hence, Statement I alone
is suffcient.
14. D) From statement I: It is not clear whether Pakistan too scored in the last 5 minutes
or not.
From Statement II: It is not clear that whether India
scored in the last 5 minutes or not.
From I and II : From both the statements, there are
two cases possible:
Case I:
Before Last 5 mins

In the last 5 mins

Final score


India

0

3

3

Pakistan

2

1

3

In this case, the match
ended in a draw.
Case II:
Before Last 5 mins

In the last 5 mins

Final score


India

1

3

4

Pakistan

3

0

3

In this case, India wins
the match.
∴ Even after combining both the statements, we can't say
whether India won the match or not.