Quant Quiz

Directions (1-5): The question given below contain two statements giving certain data. You have to decide whether the data given in the statements are sufficient for answering the questions? Mark answer - 

(1) If statement I alone is sufficient but statement II alone is not sufficient.
(2) If statement II alone is sufficient but statement I alone is not sufficient.
(3) If each statement alone (either I or II) is sufficient.
(4) If statement I and II together are not sufficient.
(5) If both statement together are sufficient, but neither statement alone is sufficient. 


1. In how many days will 6 men complete a work?
(I) 6 men and 6 women complete the work in 12 days.
(II) 8 men complete the work in 16 days.

2. What is the speed of train?
(I) The train crosses a pole in 10 seconds
(II) The train crosses a 20 m. long platform whose length is equal to in 20 seconds.

3. What is Neeta's age?
(I) Neeta is 5 years younger than her brother.
(II) The sum of their ages is 55 years.

4. Is a two-digit number odd?
(I) The sum of digit is even number.
(II) When the number is multiplied by 2, an even is obtained.

5. Is a 3 digit number divisible by 8?
(I) The number is divisible 2 and 4
(II) The number at unit's place is smaller than the number at ten's place.

Directions (6-9): Study the following information carefully and answer the questions given below. In a box there are 4 blue, 4 red, 4 white and 4 black balls.

6. If 4 balls are picked up randomly, what is the probability that all are blue?
(1) 1/1820 
(2) 1/1870
(3) 1/4
(4) 1/455
(5) None of these

7. If 4 balls are picked up randomly, whatis the probability that all are of same colour?
(1) 1/1820 
(2) 1/4
(3) 1/1870 
(4) 1/455
(5) None of these

8. If 4 balls are picked up randomly, what is the probability that not even one is white?
(1) 1819/1920 
(2) 99/364
(3) 1960/1990
(4) 1/455
(5) None of these

9. From a pack of 52 cards, 2 cards are drawn randomly. What is the probability that it has one King and one Jack?
(1) 7/663 
(2) 8/663
(3) 11/663
(4) 13/663
(5) None of these

10. In an examination a minimum marks is to be scored in each of the 8 subjects for passing. In how many ways a student can fail?
(1) 127
(2) 63
(3) 255
(4) 256
(5) None of these


ANSWERS
1. 2;
From (II)
8 × 16 = 6 × D2
D2 = (16*8)/6 = 21  Day
So, only statement (II) is sufficient.

2. 2;
From (II)
Speed = (200 + 200)/ 20 = 20 m/s

3. 5;
From (I)
Nita = Brother – 5 ...(i)
From (II)
Nita + Brother = 55  ...(ii)
From equation (i) and (ii)
Nita = 25 years
So, both statements are necessary.

4. 4;
Statement (I) is not sufficient.
Consider two-two digit number are 11 and 22. Both have sum of digits an even number. But one of the numbers is odd and the other one even. Again II is not sufficient because any number when multiplied by 2 gives an even number.

5. 4;
Statement (I) is not sufficient. Because if a number is divisible by 8 the number must be divisible by 4. But if a number is divisible by 4 it is not necessary that the number is divisible by 8 also.

Solutions (6-10)

6. 1;
Required probability = 4C4/16C4 = 1/1820

7. 4; Required probability = (4 * 4C4)/16C4 = 1/455

8. 2; Required probability = 12C4/16C4 = 495/1820 = 99/364 

9. 2;
n(S) = 52C2 = 51 × 26
n(E) = 4C1 × 4C1 = 4 × 4
P(E) = 16/(51*26) = 8/663

10. 3;
The students can fail in 1, 2, 3, 4, 5, 6, 7, 8 subjects.
So the number of ways he can fail is
8C1 + 8C2 + 8C3 + 8C4 + 8C5 + 8C6 + 8C7 + 8C8
= 8 + 28 + 56 + 70+56 + 28 + 8 + 1 = 255