Questions & Answers – (Multiple Choice) – Data Sufficiency
கொள்குறி வினா- விடைகள் – போதுமான தரவு
Directions :
Each question below is followed by two labeled facts A and B. Determine whether the data given in statements is sufficient to answer the given question.
Use the data given and in addition to your knowledge in Mathematics and every day facts for to choose the possible answer amongst (a) to (d).
Mark (a), if you can get answer for the question from (A) alone but not (B) alone.
Mark (b), if you can get answer for the question from (B) alone but not (A) alone.
Mark (c), if you can get answer for the question from (A) alone or (B) alone.
OR
Mark (c), if you can get answer for the question from both (A) and (B) together but not from (A) alone or (B) alone.
Mark (d), if you cannot get the answer for the question from (A) and (B) together but needs more data.
In these Data Sufficiency problems mostly you are not required to find the exact answer. Only yes or no.
1. Is the perimeter of a rectangle yard is greater than 60 metres?
A. The two shorter sides of the rectangle yard each 15m in size.
B. The length is 3 m longer than its width of the yard.
2. An article is discounted 15% from its selling price. What is the usual selling price of the article?
A. The discount is ₹450.
B. The discounted price is ₹2550.
3. If xy is nonzero, Is x greater than y?
A. 5x = 6y
B. x < 0
4. Robert and Rahim founded a company on jan1, 2020. In which year did the company’s profit exceeded one crore rupees?
A. In 2020, the company recorded a profit of ₹1500000. And after every year the profits double those of the previous year.
B. In 2022, the company recorded the profit of ₹6000000.
5. If z is an integer, is z an odd number?
A. z is non – negative
B. z is either a negative number or an odd number but not both
6. What is the average speed of a motor cycle as it travels 400km. between the city P and Q?
A. The motor cycle averages 70kmph for the first 3 hours.
B. The motor cycle averages 50kmph for the last 3 hours.
7. The ratio of boys to girls attended a school in 2023 is 0.75. what was the ratio of boys to girls attended the school in 2024?
A. 75 more boys attended the school than in 2023.
B. 75 more girls attended the school than in 2023.
8. ABCD is a rectangle. Is it a square?
A. BC = 12 units
B. AD = 12 units
9. When one piece of fruit is taken at random from a fruit basket, what is the probability that it is an orange?
A. There are half as many apples as oranges in the fruit basket.
B. One third of the fruits in the fruit basket are apples.
10. Is x is divisible by 140?
A. x is divisible by 2 and 5.
B. x is divisible by 4 and 7.
11.Which train is the fastest among P, Q, R and S?
A. Q is slower than R
B. P and S are slower than Q
12. X, Y and Z went to a party at different times.Who went there first?
A. Y stayed there for a short duration.
B. Z went there not later than X but not earlier than Y.
13. Is x is even?
A. 3x is odd
B. 4x is even
14. PQRS is a quadrilateral. Is QR = RS?
A. PQ = PS
B. Angle PQR = Angle PSR
15. What is the value of k?
2x + 3y = 10 ; 5x + ky = 6
A. The system has a unique solution.
B. k is non – zero.
Answers
1. a 2. c 3. c 4. a 5. c
6. d 7. d 8. d 9. c 10. c
11. c 12. b 13. a 14. c 15. d
Explanation to Answers
1. Since the perimeter = 2(l+b)
Here b = 15 ; l >15.
So l + b > 30
Hence perimeter is > 60
‘A’ alone is sufficient not considering ‘B’.
From ‘B’, l > b + 3. l and b may assume many values. So 2(l+b) may or may not be greater than 60.
Answer is ‘a’
2. From ‘A’, 15% of selling price is ₹450.It is easy to find usual selling price by finding 100%. So ‘A’ alone is sufficient not considering ‘B’.
From ‘B’, given that 85% is ₹2550. So 100% can be easily found. ‘B’ alone is sufficient not considering ‘A’.
Either ‘A ‘ or ‘ B ‘ is sufficient to answer the question. Correct option is ‘c’.
3. If xy is nonzero, then both x and y are nonzero.
From A, x = (5/6)y => If x is positive, y is also positive and y is greater than x. If x is negative, y is also negative and x is greater than y. So we cannot get yes or no for the given question and A is not sufficient to answer.
From B, when x<0 and xy is nonzero, we say y may be > 0 or < 0. And so B is not sufficient to answer.
But from both A and B, we get x and y both < 0 and x > y.
Correct choice is ‘c’.
4. From A, it is clear that the amount of profit becomes eight times in three years. Hence ‘A’ alone is sufficient to answer not considering ‘B’.
From B, the nature of growing profit is not given and hence ‘B’ alone is not sufficient to answer not considering ‘A’.
Correct option is ‘a’.
5. From A, it is clear that z is ‘0’ or positive integer. z may be odd or even integer.
So ‘A’ alone is not sufficient to answer not considering ‘B’. Similarly ‘B’ alone is not sufficient to answer not considering ‘A’.
By considering both A and B We can answer that z is an odd number.
Correct option is ‘c’
6. From the given data, it is clear that A alone or B alone is not sufficient.
Using both A and B we get the total distance covered in six hours
3×70 + 3×50 = 360. Here we don’t know the speed of the remaining distance 40km. Hence Both the statements are not sufficient to answer the question.
Correct option is ‘d’
7. Given
The ratio of boys to girls attended a school in 2023 is 3 : 4.
From the given data, it is clear that A alone or B alone is not sufficient since only addition of numbers is given. No ratio is given after addition of boys or girls. Hence Both the statements are not sufficient to answer the question.
Correct option is ‘d’
8. From the given data, it is clear that A alone or B alone is not sufficient. In a rectangle opposite sides are equal.
Here BC = AD. Equivalent statements are given. Length of AB or CD cannot be found using A or B or both.
The Correct option is ‘d’
9. From A, the ratio of apples to oranges is 0.5 : 1 = 1 : 2. So the probability of taking an orange from the basket
is (2/3). ‘A’ alone is sufficient to answer not considering ‘B’.
Likewise ‘B’ alone is sufficient to answer not considering ‘A’.
So the correct option is ‘c’.
10. From A, we say x is divisible by 10.
From B, we say x is divisible by 28.
From both A and B, we say x is divisible by Lcm of 10 and 28.
But Lcm of 10 and 28 is 140.
Hence correct option is ‘c’
11. From A, Q < R
From B, P, S < Q
Combining both, P, S < Q < R
where < denotes slower.
Hence R is the fastest train.
Hence correct option is ‘c’
12. From the given data, it is clear that A alone is not sufficient.
From B, X came after Z but Y came earlier to Z which implies that Y went there first.
Correct option is ‘b’.
13. From A, we conclude that x is odd. So ‘A’ alone is sufficient to answer not considering ‘B’.
From B, we can say x may be odd or even.
Hence the correct option is ‘a’
14. If PQ = PS, then
Angle PQS = Angle PSQ
So ‘A’ alone is not sufficient to answer not considering ‘B’. Similarly So ‘B’ alone is not sufficient to answer not considering ‘A’. But from both B and A, we get
Angle RQS = Angle RSQ => QR = RS
Correct option is ‘ c ‘.
15. Using both A and B, we cannot get exact value of k.
So correct option is ‘ d ‘
– கட்டுரையாளர், போட்டித் தேர்வு பயிற்சியாளர், குளோபல் விக்கிமாஸ்டர்; தொடர்புக்கு: success.gg@gmail.com