e-Litmus Data Sufficiency Problem in Previous Year Papers 3

Set 1

Find Solutions at the end of every section

Mark AIf the question can be answered by using one of the statements alone, but cannot be answered by using the other statements alone.Mark BIf the question can be answered by using either statement alone.Mark CIf the question can be answered by using both statements together, but cannot be answered by using the either statement alone.Mark DIf the question cannot be answered even by using both the statements together.

1.What is the number of type-2 widgets produced, if total number of widgets produced is 20,000 ?(I) If the production of type-1 widgets increases by 10% and that of type-2 decreases by 6%, the total production remains the same.(II) The ratio in which type-1 and type-2 widgets are produced is 2 : 1.(a)  A(b) B(c) C(d) D

2.How old is Sachin in 1997 ?(I)  Sachin is 11 yr  younger than Anil whose age will be a prime number in 1998.(II) Anil’s age was a prime number is 1996.(a) A(b) B(c) C (d) D

3.What is the total worth of Lakhriram’s assets ?(I) A compound interest at 10% on his assets, followed by a tax of 4% on the interest, fetches him Rs. 1500 this year.(II) The interest is compounded once every four months.(a) A(b) B(c) C(d) D

4.How many different triangles can be formed ?(I)  There are 16 co-planer straight lines.(II)  No two lines are parallel.(a) A(b) B(c) C(d) D

5.What is the selling price of the article ?(I)  The profit on sales is 20%.(II) The profit on each unit is 25% and the cost price is Rs 250.(a) A(b) B(c) C(d) D

6.What is the cost price of the article ?(I)  After selling the article, a loss of 25% on cost price is incurred.(II) The selling price is three-fourths of the cost price.(a) A(b) B(c) C(d) D

7.If p and q are the roots of the equation (ax2 + bx + c=0) then what is the value of ( p2 + q2 ) ?(I)  p + q = -b/a(II) 2pq = c/a(a) A(b) B(c) C(d) D

8.If a, b and c are integers, is (a – b + c) > (a + b – c) ?(I)  b is negative.(II) c is positive.(a) A(b) B(c) C(d) D

9.What is the ratio of the two liquids A and B in the mixture finally, if these two liquids kept in three vessels are mixed together ? (The containers are of equal volume) Assume container volume=volume of liquids(I)  The ratio of liquid A to liquid B in the first and second vessels are 3 : 5, 2 : 3 respectively.(II) The ratio of liquid A to liquid B in vessel 3 is 4 : 3.(a) A(b) B(c) C(d) D

10A tractor traveled a distance of 5 M. What is the radius of the rear wheel ?(I)  The front wheels rotates ‘N’ times more than the rear wheel over this distance.(II)The circumference of the rear wheel is ‘t’ times that of the front wheel.(a) A(b) B(c) C(d) D

Answer
1.B

2.D3.C4.D5.A6.D7.C8.C9.D10.D

Set 2

Find Solutions at the end of every section

Mark A

If the question can be answered by using one of the statements alone, but cannot be answered by using the other statements alone.

Mark B
If the question can be answered by using either statement alone.
Mark C
If the question can be answered by using both statements together, but cannot be answered by using the either statement alone.
Mark D
If the question cannot be answered even by using both the statements together.

1.What is the price of mangoes per kg ?
(I)  10 kg of mangoes and two dozen of oranges cost Rs 252.
(II) 2 Kg of mangoes could be bought in exchange for one dozen oranges.
(a) A
(b) B
(c) C
(d) D

2.What are the ages of three brothers ?
(I)  Product of their ages is 21.
(II) The sum of their ages is not divisible by 3.
(a) A
(b) B
(c) C
(d) D

3.Is n odd ?
(I) n is divisible by 3, 5, 7 and 9.
(II) 0 < n < 400
(a) A
(b) B
(c) C
(d) D

4.Two types of widget, namely type A and B are produced on a machine. The number of machine hours available per week is 80. How many widgets of type A must be produced ?
(I) One unit of type A widget requires 2 machine hours and one unit of type B widget requires 4 machines hours.
(II) The widget dealer wants to supply at least 10 units of type A widget per week and he would not accept less than 15 units of type B widget.
(a) A
(b) B
(c) C
(d) B

5.What are the values of 3 integers a, b and c ?
(I)  ab=8
(II) bc=9
(a) A
(b) B
(c) C
(d) D

6.Given that, X and Y are non-negative .What is the Value of X ?
(I) 2X + 2Y <= 40
(II) X -2Y >= 20
(a) A
(b) B
(c) C
(d) D

7.10 boys went to a neighboring orchard. Each boy stole a few mangoes.What is the total number of mangoes they stole ?
(I) The first boy stole 4 mangoes, the fourth boy stole 16 mangoes, eighth boy stole 32 mangoes and the tenth boy stole 40 mangoes.
(II) The first boy stole the minimum number of mangoes and the tenth boy stole the maximum number of mangoes.
(a) A
(b) B
(c) C
(d) D

8.What are the values of m and n ?
(I)  n is an even integer, m is an odd integer and m is greater than n.
(II) Product of m and n is 30.
(a) A
(b) B
(c) C
(d) D

9.What is the value of integer n ?
(I) n(n+1) = 6
(II) 22n = 16
(a) A
(b) B
(c) C
(d) D

10If the selling price were to be increased by 10%, the sales would reduce by 10%. In what ratio would be profits change ?
(I)  The cost price remains constant.
(II) The cost price increased by 10%.
(a) A
(b) B
(c) C
(d) D

Answer
1.C
2.D
3.C
4.C
5.D
6.D
7.D
8.C
9.A
10.A

e-Litmus Data Sufficiency Problem in Previous Year Question -2

e-Litmus Data Sufficiency Problem in Previous Year Papers 2

Set 1

Find Solutions at the end of every section

Each question is followed by two statements. You have to decide whether the information provided in the statements is sufficient for answering the question.

Mark A
If the question can be answered by using one of the statements alone, but cannot be answered by using the other statements alone.
Mark B
If the question can be answered by using either statement alone.
Mark C
If the question can be answered by using both statements together, but cannot be answered by using the either statement alone.
Mark D
If the question cannot be answered even by using both the statements together.

1. What are the ages of two individuals, X and Y ?
(I)  The age difference between them is 6 yr.
(II) The Product of their ages is divisible by 6.
(a) A
(b) B
(c) C
(d) D

2.Is x + y – z + t even ?
(I)  x + y + t is even.
(II) t and z are odd.
(a) A
(b) B
(c) C
(d) D

3.What is the number X ?
(I)  The LCM of X and 18 is 36.
(II) The HCF of x and 18 is 2.
(a) A
(b) B
(c) C
(d) D

4. What is the length of the rectangle ABCD ?
(I)  Area of rectangle is 48 sq. unit.
(II) Length of diagonal is 10 unit.
(a) A
(b) B
(c) C
(d) D

5. What is the first term of an arithmetic progression of positive integers ?
(I)  Sum of the squares of the first and the second term is 116.
(II)The fifth term is divisible by 7.
(a) A
(b) B
(c) C
(d) D

6. What is the price of bananas ?
(I)  With Rs 84, I can buy 14 bananas and 35 oranges.
(II) If price of bananas is reduced by 50%,then we can buy 48 bananas in Rs 12.
(a) A
(b) B
(c) C
(d) D

7. What is the area of the triangle ?
(I)  Two sides are 41 cm each.
(II) The altitude to the third side is 9 cm long.
(a) A
(b) B
(c) C
(d) D

8. What is the profit percentage ?
(I)  The cost price is 80% of the selling price.
(II) The profit is Rs 50.
(a) A
(b) B
(c) C
(d) D

9. What is the value of x, if x and y are consecutive positive even integers ?
(I)  (x – y)2 = 4
(II) (x + y)2≤ 100
(a) A
(b) B
(c) C
(d) D

10. If x, y and z are real numbers, is z-x is even or odd ?
(I)  xyz is odd.
(II) xy + yz + zx is even.
(a) A
(b) B
(c) C

(d) D

Answer

1.D

2.C

3.C

4.C

5.A

6.A

7.C

8.A

9.D

10.A

Set 2

Find Solutions at the end of every section

Each question is followed by two statements. You have to decide whether the information provided in the statements is sufficient for answering the question.

Mark A

If the question can be answered by using one of the statements alone, but cannot be answered by using the other statements alone.

Mark B

If the question can be answered by using either statement alone.

Mark C

If the question can be answered by using both statements together, but cannot be answered by using the either statement alone.

Mark D

If the question cannot be answered even by using both the statements together.

1.What is the cost price of the chair ?

(I) The chair and the table are sold,respectively, at profits of 15% and 20%.

(II) If the cost price of the chair is increased by 10% and that of the table is increased by 20%,the profit reduces by Rs 20.

(a) A

(b) B

(c) C

(d) D

2.What is the area bounded by the two lines and the co-ordinates axes in the first quadrant ?

(I)  The lines intersect at a point which also lies on the lines 3x – 4y = 1 and 7x – 8y = 5.

(II) The lines are perpendicular and one of them intersects the Y-axis at an intercept of 4.

(a) A

(b) B

(c) C

(d) D

3.What is the ratio of the volume of the given right circular cone to the one obtained from it ?

(I) The smaller cone is obtained by passing a plane parallel to the base and dividing a the original height in the ratio of 1 : 2.

(II) The height and the base of the new cone are one-third those of the original cone.

(a) A

(b) B

(c) C

(d) D

4.What is the speed of the car ?

(I)   The speed of a car is 10 more than that of the a motorcycle.

(II) The motorcycle takes 2 Hours more than the car to cover 100 Km.

(a) A

(b) B

(c) C

(d) D

5.Three friends P, Q and R are wearing hats,either black or white. Each person can see the hats of the other two persons. What is the color of P’s hat ?

(I)  P says that he can see one black hat and one white hat.

(II) Q says that he can see one white hat and one black hat.

(a) A

(b) B

(c) C

(d) D

6.What are the values of x and y ?

(I)   3x + 2y = 45

(II) 10.5x + 7y = 157.5

(a) A

(b) B

(c) C

(d) D

7.What are the values of 3 integers a, b and c ?

(I) ab=8

(II) bc =9

(a) A

(b) B

(c) C

(d) D

8.Is the number completely divisible by 99 ?

(I) The number is divisible by 9 and 11 simultaneously.

(II) If the digits of the numbers are reversed, the number is divisible by 9 and 11.

(a) A

(b) B

(c) C

(d) D

9.What is the value of a3 + b3 ?

(I)  a2 + b2 = 22

(II) ab=3

(a) A

(b) B

(c) C

(d) D

10After what time will the two persons Tez and Gati meet while moving around the circular track? Both of them start at the same point and at the same time ?

(I) Tex moves at a constant speed of 5 m/s , while Gati starts at a speed of 2m/s and increases his speed by 0.5m/s at the end of every second thereafter.

(II) Gati can complete one entire lap in exactly 10s.

(a) A

(b) B

(c) C

(d) D

Answer

1.D

2.A

3.B

4.C

5.D

6.D

7.D

8.B

9.D

10.D

e-Litmus Data Sufficiency Problem in Previous Year Question

e-Litmus Data Sufficiency Problem in Previous Year Papers 1

Set 1

Find Solutions at the end of every section


Each question is followed by two statements. You have to decide whether the information provided in the statements is sufficient for answering the question.
Mark A
If the question can be answered by using one of the statements alone, but cannot be answered by using the other statements alone.
Mark B
If the question can be answered by using either statement alone.
Mark C
If the question can be answered by using both statements together, but cannot be answered by using the either statement alone.
Mark D
If the question cannot be answered even by using both the statements together.

Question 1: Who among P, Q, T, V and M is exactly in the middle when they are arranged in ascending order of their heights?
Statements:

V is taller than Q but shorter than M.
T is taller than Q and M but shorter than P.
A. I alone is sufficient while II alone is not sufficient
B. II alone is sufficient while I alone is not sufficient
C. Either I or II is sufficient
D. Neither I nor II is sufficient
E. Both I and II are sufficient

From I, we have: M > V > Q.From II, we have: T > Q, T > M, P > T.Combining the above two, we have: P>T>M>V>Q i.e. Q<v<m<t<p.< p=””>Clearly, M is in the middle.

2.
What is the value of |x|?
Statement.(1)
x = -|x| .
Statement.(2)
x2 = 4.
(a) A
(b) B
(c) C
(d) D

Expl. of Statement (1)

The absolute value of x, |x|, is always positive or 0, so this only determines that x is negative or 0; NOT SUFFICIENT.
Expl. of Statement (2)

Exactly two values of x (x= ±2) are possible, each of which gives the value 2 for |x| SUFFICIENT.
 Answer
(A)  [Each statement alone is not sufficient.]

Question: Which code word stands for ‘good’ in the coded sentence ‘sin co bye’ which means ‘He is good?
Statements:

In the same code language, ‘co mot det’ means ‘They are good’.
In the same code language, ‘sin mic bye’ means ‘He is honest’.
A. I alone is sufficient while II alone is not sufficient
B. II alone is sufficient while I alone is not sufficient
C. Either I or II is sufficient
D. Neither I nor II is sufficient
E. Both I and II are sufficient

Explanation: In the given statement and I, the common word is ‘good’ and the common code word is ‘co’. So, ‘co’ is the code for ‘good’.In the given statement and II, the common words are ‘He’ and ‘is’ and the common code words are ‘sin’ and ‘bye’. So ‘sin’ and ‘bye’ are the codes for ‘He’ and ‘is’. Thus, in the given statement, ‘co’ is the code for ‘good’.

4.
If x is negative, is x < – 3 ?
Statement. (1)
x2  > 9.
Statement. (2)
x3 < -9.
(a) A
(b) B
(c) C
(d) D

Expl. of Statement (1)

Given that  x2> 9, it follows that x < -3 or x > 3, a result that can be obtained in a variety of ways. For example, consider the equivalent equation (|x|) >9 that reduces to |x| >3,or consider when the two factors of x2 —9 are both positive and when the two factors of x2 —9 are both negative, or consider where the graph of the parabola y = x2 – 9 is above the x-axis, etc. Since it is also given that x is negative, it follows that
x< -3; SUFFICIENT.
Expl. of Statement (2)

Given that x3 < -9, if x = -4, then x3  = -64, and so x3 <-9 and it is true that  x < -3. However, if x = —3, then x = —27, and so x3  < —9, but it is not true that x < —3; NOT SUFFICIENT.
 Answer
(A)  [Each statement alone is not sufficient.]

5.
If x and y are integers, is xy even?
Statement. (1)
x = y + l
Statement. (2)
x/y is an even integer..
(a) A
(b) B
(c) C
(d) D

Expl. of Statement  (1)

Determine if xy is even; Since x and y are consecutive integers, one of these two numbers is even, and hence their product is even. For example, if x is even, then x = 2m for some integer m, and thus xy =(2m)y =(my)(2), which is an integer multiple of 2, so xy is even; SUFFICIENT.
Expl. of Statement  (2)

If x /y is even, then x/y= 2n for some integer n, and thus x = 2ny. From this it follows that xy =(2ny)(y) =(ny2)(2), which is an integer multiple of 2, so xy is even; SUFFICIENT.
 Answer
(B)  [Each statement alone is  sufficient.]

6.
Paula and Sandy were among those people who sold raffle tickets to raise money for Club X. If Paula and Sandy sold a total of 100 of the tickets, how many of the tickets did Paula sell?
Statement. (1)
Sandy sold 2/3 as many of the raffle tickets as Paula did
Statement. (2)
Sandy sold 8 percent of all the raffle tickets sold for Club X..
(a) A
(b) B
(c) C
(d) D

Expl. of Statement  (1)

If Paula sold p tickets and Sandy sold s tickets, then p + s = 100. Since Sandy sold 2/3 as many tickets as Paula, s= (2/3)p. The value of p can be determined by solving the two equations simultaneously; SUFFICIENT.
Expl. of Statement  (2)

Since the total number of the raffle tickets sold is unknown, the number of tickets that Sandy or Paula sold cannot be determined NOT SUFFICIENT.
 Answer
(A)  [Each statement alone is not  sufficient.]

7.
What is the number of cans that can be packed in a certain carton?
Statement. (1)
The interior volume of this carton is 2,304 cubic inches
Statement. (2)
The exterior of each can is 6 inches high and has a diameter of 4 inches
(a) A
(b) B
(c) C
(d) D

Expl. of Statement  (1)

No information about the size of the cans is given; NOT SUFFICIENT.
Expl. of Statement  (2)

No information about the size of the carton is given; NOT SUFFICIENT.
 Taking (1) + (2) Together
Taking (1) and (2) together, there is still not enough information to answer the question. If the carton is a rectangular solid that is 1 inch by 1 inch by 2,304 inches and the cans are cylindrical with the given dimensions, then 0 cans can be packed into the carton. However, if the carton is a rectangular solid that is 16 inches by 12 inches by 12 inches and the cans are cylindrical with the given dimensions, then 1 or more cans can be packed into the carton.
 Answer
(D)  [Each statement alone and together is not sufficient.]

Set 2

Find Solutions at the end of every section

Each question is followed by two statements. You have to decide whether the information provided in the statements is sufficient for answering the question.
Mark A
If the question can be answered by using one of the statements alone, but cannot be answered by using the other statements alone.
Mark B
If the question can be answered by using either statement alone.
Mark C
If the question can be answered by using both statements together, but cannot be answered by using the either statement alone.
Mark D
If the question cannot be answered even by using both the statements together.


1.
If n is an integer, is n even ?
Statement.(1)
n^2 -1 is an odd integer.
Statement.(2)
3n + 4 is an even integer.
(a) A
(b) B
(c) C
(d) D

Expl. of Statement (1)
Since n2 —1 is odd, n2 is even and so n is even; SUFFICIENT.

Expl. of Statement (2)

Since 3n+ 4 is even, 3n is even and so n is even; SUFFICIENT.
 Answer
(B)  [Each statement alone is sufficient.]

2.
If n is an integer, is n+ 1 odd ?
Statement. (1)
n+ 2 is an even integer.
Statement. (2)
n-1 is an odd integer.
(a) A
(b) B
(c) C
(d) D
Expl. of Statement (1)

Since n+ 2 is even, n is an even integer, and therefore n+1 would be an odd integer; SUFFICIENT.
Expl. of Statement (2)

Since n-1 is an odd integer, n is an even integer. Therefore n+ 1 would be an odd integer; SUFFICIENT.
 Answer
(B)  [Each statement alone is sufficient.]

3.
Is x a negative number?
Statement. (1)
9x > 10x.
Statement. (2)
x + 3 is positive.
(a) A
(b) B
(c) C
(d) D
Expl. of Statement  (1)

Subtracting 9x from both sides of 9x  > lOx gives 0 > x, which expresses the condition that x is negative; SUFFICIENT.
Expl. of Statement  (2)

Subtracting 3 from both sides of x+ 3 > 0 gives x > -3, and x > -3 is true for some negative numbers (such as -2 and -1) and for some numbers that aren’t negative (such as 0 and 1); NOT SUFFICIENT.
 Answer
(A)  [Each statement alone is  not sufficient.]

4.
What is the tens digit of positive integer x?
Statement. (1)
x divided by 100 has a remainder of 30.
Statement. (2)
x divided by 110 has a remainder of 30.
(a) A
(b) B
(c) C
(d) D

Expl. of Statement  (1)

Having a remainder of 30 when x is divided by 100 can only happen if x has a tens digit of  3 and a ones digit of 0, as in 130, 230, 630, and so forth; SUFFICIENT.
Expl. of Statement  (2)

When 140 is divided by 110, the quotient is 1 R 30. However, 250 divided by 110 yields a quotient of 2 R 30, and 360 divided by 110 gives a quotient of 3 R 30. Since there is no consistency in the tens digit, more information is needed; NOT SUFFICIENT.
 Answer
(A)  [Each statement alone is not  sufficient.]

5.
If k is an integer such that 56 < k < 66, what is the value of k?
Statement. (1)
If k were divided by 2, the remainder would be 1.
Statement. (2)
If k + 1 were divided by 3, the remainder would be O.
(a) A
(b) B
(c) C
(d) D

Expl. of Statement  (1)

Determine the value of the integer k, where 56<k< 66 It is given that the remainder is 1 when k is divided by 2, which implies that k is odd Therefore, the value of k can be 57, 59, 61,63, or 65; NOT SUFFICIENT.
Expl. of Statement  (2)

It is given that the remainder is 0 when k + 1 is divided by 3, which implies that k + 1 is divisible by 3. Since 56 <k <66 (equivalently, 57 <k+1 <67), the value of k + 1 can be 60, 63, or 66 so the value of k can be 59, 62 or 65; NOT SUFFICIENT.
 Taking (1) + (2) Together

Taking (1) and (2) together, 59 and 65 appear in both lists of possible values for k; NOT sufficient.
 Answer
(D)  [Each statement alone and together is not sufficient.]