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.
   
   
    
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:


6. 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
   
   
    



7. 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
   
   
    



8. 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
   
   
    



9. 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
   
   
    



10. 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