# Mixed Quantitative Aptitude Questions Set 162

Directions(1-5): Find the values of x and y, compare their values and choose a correct option.

1. (i) 3x² + 11x + 10 = 0
(ii) 2y² + 11y + 14 = 0
x > y
y > x
x >= y
No relation between x and y.
y >= x
Option C
(i) 3x² + 11x + 10 = 0
3x² + 6x + 5x + 10 = 0
3x (x + 2) + 5 (x + 2) = 0
x = – 2, –5/3
(ii) 2y² + 11y + 14 = 0
2y² + 7y + 4y + 14 = 0
y (2y + 7) +2 (2y + 7) = 0
y = –2, – 7/2
x ≥ y

2. (i) 2x² + 9x + 9 = 0
(ii) 15y² + 16y + 4 = 0
y >= x
x >= y
No relation between x and y.
y > x
x > y
Option D
(i) 2x² + 9x + 9 = 0
2x² + (6 + 3) x + 9 = 0
2x (x + 3) + 3 (x + 3) = 0
x = –3/2 , –3
(ii) 15y² + 16y + 4 = 0
15y² + 10y + 6y + 4 = 0
5y (3y + 2) + 2 (3y + 2) = 0
y = –2/5 , –2/3
x < y

3. (i). x² – 17x + 72 = 0
(ii). 6y² – 31y + 35 = 0
No relation between x and y.
x > y
y > x
x >= y
y >= x
Option B
x² – 17x + 72 = 0
x = 8, 9
6y² – 31y + 35 = 0
y = 1.6, 3.5
x>y

4. (i). x² – 37x + 300 = 0
(ii). y² – 43y + 372 = 0
x > y
y >= x
No relation between x and y.
y > x
x >= y
Option C
x² – 37x + 300 = 0
x = 25, 12
y² – 43y + 372 = 0
y = 31, 12
No relation between x and y.

5. (i) 12x² + 11x + 2 = 0
(ii) 12y²+ 7y + 1 = 0
x >= y
y >= x
y > x
x > y
No relation between x and y.
Option E
(i) 12x² + 8x + 3x + 2 = 0
4x (3x + 2) + 1 (3x + 2) = 0
x = –2/3 , –1/4
(ii) 12y² + 7y + 1 = 0
12y² + 4y + 3y + 1 = 0
4y (3y + 1) +1 (3y + 1) = 0
y = –1/3 , –1/4
No relation between x and y.

6. Directions(6-10): Read the following graph carefully and answer the questions given below: Delhi University offers two courses PG and PhD. The information regarding number of students applied for these two courses and among how many got selected from year 2004-2009 are shown by the graph given below:

7. Average number of students got selected for PhD program is by what percent more/less the average number of students applied for PG programs.
65% less
77% less
68% less
72% less
70% less
Option D
Average students selected for PhD program = (2160+4550+2850+4455+3402+3900)/6
= 21317/6 = 3553 (approx)
Average number of student applied for PG program
= (8000+17000 +10000 +14000 +16500 +11000)/6
= 76500/6 = 12750
Required percentage = (12750 −3553)/12750 × 100 = 72% less

8. Which year shows the highest quantum difference between the number of students applied and got selected for PhD programs.
2008
2006
2009
2007
2005
Option C
Difference for year 2004 = 4000 − 2160 = 1840
For year, 2005 = 13000 −4550 = 8450
For year, 2006 = 6000 − 2850 = 3150
For year, 2007 = 9000 − 4455 = 4545
For year, 2008 = 13500 −3402 = 10098
For year, 2009 = 15000 −3900 = 11100
2009

9. What is the respective ratio of the percentage increase/decrease in the students got selected for PG in 2005 over Year 2004 to the percentage increase/decrease in the number of students applied for PhD in year 2008 over year 2007.
47 ∶ 14
47 ∶ 10
49 ∶ 12
41 ∶ 10
47 ∶ 13
Option B
Percentage increase in selected students in PG in 2005= (6035−1800)/1800 × 100 = 235%
Percentage increase in number of applied students in PhD in 2008 = (13500 −9000)/9000 × 100 = 50%
Required ratio = 235 ∶ 50 = 47 ∶ 10

10. Find the ratio of Number of students selected in 2005, 2007 and 2009 for PhD course to number of students applied in 2004, 2006 and 2008 for same course.
2647 ∶ 4400
2551 ∶ 4300
2577 ∶ 4700
2581 ∶ 4700
2581 ∶ 4100
Option D
Number of students selected in 2005, 2007 and 2009 for PhD course
= 13000 × 35/100 +9000 × 49.5/100 + 15000 × 26/100
= 4550 +4455 +3900 = 12905
Number of students applied in 2004, 2006 and 2008 for PhD course
= 4000 + 6000 +13500 = 23500
Ratio = 12905 ∶ 23500 = 2581 ∶ 4700

11. In PG program which year shows highest percentage increase/decrease in number of student selected over previous year?
2006
2009
2007
2005
2008
Option D
Percentage increase/decrease in the number of selected students
For year 2005 = 6035−1800/1800 × 100 = 235%
For year 2006 = 6035−2350/6035 × 100 = 61%
For year 2007 = 6370−2350/2350 × 100 = 171%
For year 2008 = 9570−6370/6370 × 100 = 50%
For year 2009 = 9570−5280/9570 × 100 = 44.8%
2005