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## Sunday, 14 February 2016

### 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.
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. Ratio of votes got by Rahul and Naresh is 3:1 and  and the difference between their votes was  36% of total votes.
Explanation:
Using statement I alone:
It is given that Naresh got 30% of the votes.
But number of candidates contested in the election is not given.
Hence Rahul may or may not have majority of votes.
Hence statement I alone is not sufficient to answer the questions.
Using statement II alone:
Given ratio of votes got by Rahul and Naresh is  3 :1.
Given difference between their votes 3x –x =>2x = 36% of the 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

2.    The profits earned by a XYZ company in 2016 were Rs. 3 lakhs. What was the profit earned in 2015?
1. In 2016 ,the  expenditure was 25% more than in 2015
2. In 2016, the revenue was 25% more than in 2015
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 Mathematics test.
2. A total of 200 questions papers were given to all students in the class.
Explanation:
Each student was given only test, either Mathematics or Physics
Taking statement 1 alone:
Here 40% 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 the village B was what percentage of the initial population of the village A ?
1.            The increased population of village A was equal to the initial population of the village B.
2.            The increase in the population of the village A  was  $\frac{12}{11}$ the decrease in the population of village B
Explanation :
Let initial population of village A be A and B be B.
A’s population is increased by 20%=> Population after 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,
Increased population of A = Initial population of B
ð  $\frac{120}{100}$ 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
Required percentage can be found by =
Decreased population of village B / Initial 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
Explanation: Sharma spending 72% of his income after tax
Taking statement 1 alone,
Sharma got 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, 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%.
Explanation :
Let the total number of candidates appeared for the interview be N.
Taking statement 1 alone
Iit 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 the information about qualified candidates.
44 more candidates qualified, the qualified percentage would have been 62%.
We cannot find answer for 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 distinction in the examination
Explanation :
Given that number of students is 100 and all 100 students took the exam.
Taking statement 1 alone:
Exactly 20 girls got distinction. From this we cannot find how many boys got distinction, because we don’t know number of  boys and  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 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 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%
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 intial price and expenditure, we cannot find by what percentage consumption should be reduced
From Statement 2 alone:
Let us assume 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.
Explanation:
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 1st year, . thrice the number of matches he played in 2nd year and 4 times the number of matches he played are equal
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 2nd 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 1st year= 3 times the 2nd year= 4 times the 3rd year
Ratio of matches in 3 years =>
1 / 2
:
1 / 3
1 / 4
=>12: 8:6 =>6:4:3
Here proportion of matches is given, but number of matches won in 2nd and 3rd years is not known
Hence statement 2 alone is not sufficient to answer the question
Combining both statements 1 and 2 together:
We have percentage of matches won in each year and 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 few questions on data sufficiency on percentages