Quant Quiz

Directions (Q. 1 to 5): In each of these questions, two equations numbered I and II are given. You have to solve both the equations and answer.

(1) if x < y

(2) if x ≤y

(3) if x > y

(4) if x ≥ y

(5) if x = y or the relationship cannot be established.

Question.1. 
I. x^2 + 13x + 42 = 0
II. y^2 + 19 y + 9 0 = 0

Question.2. 
I. x^2 +15x + 56 = 0
II. y^2 -23 y + 132 = 0

Question.3. 
I. 3x^2 + 7x + 4 = 0
II. 2y^2 + 6y + 4 = 0

Question.4. 
I. 12x^2 – 22x + 10 = 0
II. 14y^2 – 26y + 12 = 0

Question.5. 
I. 8x^2 + 12x + 4 = 0
II. 9y^2 + 17y + 8 = 0

Directions for questions 6 to 10: Answer the questions on the basis of the information given below.

The table given below shows the production of two types of items by four different companies in six different months of a year.

(Table ▲)

Question.6. In which month was the difference between the number of items of Type-1 produced by company-M and that of Type-2 produced by company-N the second lowest?
1) January
2) February
3) March
4) April
5) May

Question.7. What was the average number of items of Type-2 produced by all the companies together in month of January?
1) 498.5
2) 489.5
3) 469.5
4) 496.5
5) None of these

Question.8. What was the respective ratio between the number of items of Type-2 produced by company-M in the month of May and the number of items of Type-1 produced by company-L in the month of March?
1) 49 : 109
2) 31 : 48
3) 50 : 109
4) 43 : 58
5) None of these

Question.9. Number of items of Type-1 produced by company-N in April was approximately what percent of the number of items of Type-2 produced by company-M in March?
1) 145
2) 150
3) 140
4) 160
5) 155

Question.10. What was the approximate percent decrease in the number of items of Type-2 that company-K produced in June as compared to previous month?
1) 30
2) 25
3) 22
4) 40
5) 35

Solutions:

Solutions for Question (1 – 5):

Answer.1. 3;
On solving equation (I)
x = –6, –7
On solving equation (II)
y = –9, –10
Hence, (x > y).

Answer.2. 1; 
On solving equation (I)
x = –7, –8
On solving equation (II)
y = 11, 12
Hence, (x < y).

Answer.3. 5;
On solving equation (I)
x = –1, –4/3
On solving equation (II)
y = –1, –2
Hence, relationship cannot be established.

Answer.4. 5;
On solving equation (I)
x = 1, 5/6
On solving equation (II)
y = 1, 6/7
Hence, relationship cannot be established.

Answer.5. 5;
On solving equation (I)
x = –1, – 1/2
On solving equation (II)
y = –1, – 8/9
Hence, relationship cannot be established.

Solutions for Question (6 – 10):

Answer.6. 2;
Difference between number of items of Type-1 produced by company-M and that of Type-2 produced by company-N:
In January = 564 – 434 = 130
In February = 544 – 532 = 12
In March = 765 – 765 = 0
In April = 809 – 665 = 144
In May = 544 – 424 = 120
In June = 568 – 546 = 22
∴ The difference is second lowest in the month of February.

Answer.7. 1;
Required Average = (452 + 654 + 324 + 564)/4 = 498.5

Answer.8. 5;
Required ratio = 666 : 864 = 37 : 48.

Answer.9. 5;
Required Percentage = 875/565 x 100 = 155%

Answer.10. 5; 
Required Percentage Decrease = (656 – 426)/656 x 100
= 230/656 x 100 = 35%