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Data Sufficiency Questions for GMAT, CAT- Percentages

*Directions for the questions on data sufficiency:*
A. Statement 1 ALONE is sufficient,
but statement 2 alone is not sufficient to answer the question asked.

B. Statement 2 ALONE is sufficient,
but statement 1 alone is not sufficient to answer the question asked.

C. BOTH statements (1) and (2)
TOGETHER are sufficient to answer the question asked, but NEITHER statement
ALONE is sufficient.

D. EACH statement ALONE is
sufficient to answer the question asked.

E. Statements (1) and (2) TOGETHER
are NOT sufficient to answer the question asked, and additional data specific
to the problem are needed.

*1.**In an election, did Rahul get the majority of the votes?*

*1**.*

*Naresh got 30% of the votes.*

*2**. The ratio of votes got by Rahul and Naresh is 3:1 and the difference between their votes was 36% of total votes.*

**Answer :B**

**Explanation:**

__Using statement I alone:__
It is given that Naresh
got 30% of the votes.

But the number of candidates contested in the election is not given.

Hence Rahul may or may not have the majority of
votes.

Hence statement I
alone is not sufficient to answer the questions.

__Using statement II alone:__
Given the ratio of
votes got by Rahul and Naresh is 3: 1.

Then Rahul’s votes are
3x and Naresh’s votes are x.

Given difference
between their votes 3x –x =>2x = 36% of the votes

x= 18% of votes

So Rahul got 3x= 3x 18% =54% of total votes.

So Rahul got 54%
votes and all other got 46% of votes

Hence, Rahul got
majority of votes.

Hence, statement II
alone is sufficient to answer the question

**The profits earned by an XYZ company in 2016 were Rs. 3 lakhs. What was the profit earned in 2015?**

*2.***1.**In 2016 ,the expenditure was 25% more than in 2015

**2**. In 2016, the revenue was 25% more than in 2015

**Answer: C**

**Explanation:**

Given XYZ Company’s
profits in 2016 were Rs 3 lacs.

Means the
difference between revenue and expenditure is 3 lacs.

__Taking statement 1 alone,__
Expenditure in 2016
= Expenditure in 2015 x

125
100

Here we have
information only about expenditures so we cannot find the profits earned in
2015

__Taking statement 2 alone,__
Revenue in 2016 =
Revenue in 2015 x

125
100

Here information
about revenues only given.

This information is
not sufficient to find the profits in 2015

__Combining both statements 1 and 2 together__
The ratio of
expenditures in 2015 and 2016 = 4:5

The ratio of
revenues in 2015 and 2016 = 4:5

Now we can find the
profits in 2015

Hence both statements
together are needed to find the answer.

*3.**In a class, each of the students was given either a Mathematics test or a Physics test. How many of the students were given a Physics test?*

*1.**40% of the students were given the Mathematics test.*

*2.**A total of 200 questions paper was given to all students in the class.*

**Answer: C**

**Explanation:**

Each student was given the only test,
either Mathematics or Physics

__Taking statement 1 alone:__
Here 40% of students took Mathematics test, and then 60% of the students
took Physics test. But the total number of students is unknown.

So statement 1 alone is not sufficient to answer the question

__Taking statement 2 alone,__
Statement 2 gives the total number of students is 200.

But the proportion of Mathematics and Physics is not known.

Hence statement 2 alone is not sufficient.

__Combining both statements I and II together__
Total number of students is 200 and the number of students who took
physics are 60% of the total students

Hence, both statements together are needed to answer the question.

*4.**The population of village A increased by 20% over the same time period, that the population of the village B decreased by 20%. The decreased population of village B was what percentage of the initial population of the village A?*

*1.**The increased the population of village A was equal to the initial population of village B.*

*2.**The increase in the population of the village A was $\frac{12}{11}$ the decrease in the population of the village B*

**Answer : D**

**Explanation :**

Let the initial population of village A be A and B be B.

A’s population is increased by 20%=> Population after the increase is

120
100

of A
B’s population is decreased by 20% => Population after decrease is

80
100

of B

__Taking statement 1 alone,__
The increased population of A = The initial population of B

Ã° $\frac{120}{100}$
A = B

Initial population
of village A =

100
120

B
Now we can find the required percentage =>

Decreased population of village B
Increased population of village A

x 100%
= $ \frac{\frac{80B}{100}}{\frac{100B}{120}}$
x 100% =

80
100

X
100
120

So statement 1 alone is sufficient to answer the question

__From statement 2 alone,__
From statement II,

20
100

A =
12
11

x
20
100

B
Now we can find the A =

12
11

B
The required percentage can be found by =

Decreased population of village B
Increased population of village A

x 100% = $ \frac{\frac{80B}{100}}{\frac{12B}{11}}$ x 100%
Similarly, statement II alone is sufficient to answer the question.

*5.**What is Sharma’s salary, if he spends 72% of his income after paying tax?*

*1.**Sharma got tax exemption of Rs. 70,000*

**2.**

*Sharma paid 10% of his income as tax*

**Answer: E**

**Explanation:**Sharma spending 72% of his income after tax

__Taking statement 1 alone,__
Sharma got a tax exemption of Rs 70000. We can find his income using this information

So statement 1 alone is not sufficient

__Taking statement 2 alone,__
Sharma paid 10% of income as tax.

Here we don’t know how much he paid as tax in rupees. So we can find
Sharma’s income using statement 2 alone.

__Combining both statement 1 and 2 together,__
We can find his salary, because
we don’t have any information about the tax he paid

Using both statements together, the answer can’t be found.

*6.**How many candidates appeared for the interview?*

*1.**Only 40% of candidates are qualified in the interview*

*2.**If 44 more students qualified, the qualified percentage would have been 62%.*

**Answer : C**

**Explanation :**

Let the total number of candidates appeared for the interview be N.

__Taking statement 1 alone__
It gives only information about what percent of candidates are qualified in the
interview

We cannot find the total number of candidates using statement 1 alone

__Taking Statement 2 alone,__
It will give information about qualified candidates.

44 more candidates qualified, the qualified percentage would have been 62%.

We cannot find an answer for the question using statement 2 alone

__Combining the statements I and II, we get__
40
100

N + 44 =
62
100

N
Hence, N can be
calculated.

So both statements together are needed

*7.**In a class of 100 students, how many boys got distinction in an examination, if all of them took the exam?*

*1.**Exactly 20 girls got distinction in the examination.*

*2.**$\frac{3}{5}$ of the class got a distinction in the examination*

**Answer : C**

**Explanation :**

Given that the number of students is 100 and all 100 students took the exam.

__Taking statement 1 alone:__
Exactly 20 girls got a distinction. From this, we cannot find how many boys
got the distinction, because we don’t know the number of boys and the number of girls in the class.

Hence statement 1 alone is not sufficient to answer the question

__Taking statement 2 alone :__
3
5

of the class got the distinction
3
5

x 100 = 60 students got distinction in the class. But we don’t know
how many of these are girls and boys?
So statement 2 alone is not sufficient to answer the question.

__Combining both statement 1 and 2 together:__
60 students got distinction and of them 20 are girls.

So 40 boys got the distinction.

So both statements together are needed to find the answer

*8.**If the price of sugar increases by 25%, by what percentage should the consumption be reduced?*

*1.**Before the price hike, consumption of sugar was 20 kgs per month*

*2.**Because of increase, total expenditure on sugar increases by 20%*

**Answer: B**

**Explanation:**

Price of
sugar increased by 25%

__From statement 1 alone:__
The
consumption of sugar per month was 20 kgs. We don’t know the initial price and expenditure,
we cannot find by what percentage consumption should be reduced

__From Statement 2 alone:__
Let us
assume the original price of sugar per kg be Rs 10 and original consumption be Rs
10

Total
expenditure = 10 x 10 = Rs 100

Price is
increased by 25% and expenditure is increased by 20%.

New price
and expenditure would be Rs 12.5 and Rs 120 respectively

Let us take
new consumption be x, then x

x =

120
12.5

= 9.6
Hence
reduction in consumption =

0.4
10

x 100 % = 4%
Hence,
statement 2 alone is sufficient to answer the question.

*9.**The income of Sudheer is Rs 7,50,000 in the year 2016. What was his income in 2015?*

*1.**Income is increased by 40% in 2016 as compared to 2015.*

*2.**Income in 2015 increased by 30% as compared to 2014.*

**Answer: A**

**Explanation:**

The given income of Sudheer in 2016 is Rs 7,50,000.

__Taking statement 1 alone :__
Let the salary of Sudheer in 2015 be N,

Income is increased by 40% in 2015 as compared to
2015

=> N x

140
100

>
= Rs 7,50,000
=> 1.4N = 7,50,000

=> N = Rs
5,35,714

Hence
statement 1 alone is sufficient to answer the question

__Statement 2 alone :__
Income of
2015 increased by 30% as compared to 2014.

Income in
2015 is 1.3 times the income in 2014.

But we don’t
know the income in 2014 and 2015 as well

Hence
statement 2 alone is not sufficient to answer the question.

*10.**Mr. Ravi Shastri was a captain of a cricket team for three consecutive years. As captain, he lost 40% of during his first year. If he played no tie matches, what was his overall winning percentage in 3 years?*

*1.**He won 63% of her matches in her second year and lost 36% of matches in the 3 rd year.*

*2.**Twice the number of matches he played is 1*

^{st}year, . thrice the number of matches he played in 2^{nd}year and 4 times the number of matches he played are equal**Answer : C**

**Explanation :**

Mr. Shastri lost 40% during his first year. As no tie matches are there,
he won 60% of matches in 1 st year

__Taking statement 1 alone:__
He won 63% of matches in 2

^{nd}year and lost 36% of matches in 3 rd years.
Number of matches he won in 3 years is 60%, 63% and 64% of matches

But we don’t know how many matches he played in each year.

So statement 1 alone is not sufficient to answer the question.

__Taking statement 2 alone:__
The ratio of matches in 3 years => 2 times the 1

^{st}year= 3 times the 2^{nd}year= 4 times the 3^{rd}year
The ratio of matches in 3 years =>

1
2

:
1
3

:
1
4

=>12: 8:6 =>6:4:3
Here the proportion of matches is given, but the number of matches won in 2

^{nd}and 3^{rd}years is not known
Hence statement 2 alone is not sufficient to answer the question

__Combining both statements 1 and 2 together:__
We have a percentage of matches won
in each year and the ratio of matches played each year.

Overall winning percentage is the weighted average of percentage won in
the 3 years, with the number of matches being the weights.

*Data sufficiency questions on percentages are very useful for exams like GMAT Maths, CAT Quantitative aptitude, SBI Bank PO Exams, IBPS PO exams, SBI Clerks exam and IBPS Clerks exams. And most of the companies are asking a few questions on data sufficiency on percentages*