Quantitative Aptitude: Inequalities Set 3

Directions: Each question below contains a statement followed by Quantity I and Quantity II. Find both to find the relationship among them. Mark your answer accordingly.

1. If the perimeter of square and circle is same, then
   Quantity I: the area of square
   Quantity II: the area of circle
   A) Quantity I > Quantity II
   B) Quantity I ≥  Quantity II
   C) Quantity II > Quantity I
   D) Quantity II ≥  Quantity I
   E) Quantity I = Quantity II or Relation cannot be established
   
   View Answer

      Option C
   Solution:
   When perimeter of square, circle and rectangle are equal then area in descending order is
   area of circle > area of square > area of rectangle
   Hence II > I 
2. The principal amount is Rs 12,000
   Quantity I: Simple Interest on the sum at the rate of 10% per annum for 3 years
   Quantity II: Compound Interest on the sum at rate of 10% compounded semi-annually for one and a half year.
   A) Quantity I > Quantity II
   B) Quantity I ≥  Quantity II
   C) Quantity II > Quantity I
   D) Quantity II ≥  Quantity I
   E) Quantity I = Quantity II or Relation cannot be established
   
   View Answer

      Option A
   Solution:
   I: SI = 3*10% = 30% of 12000 = Rs 3600
   II: CI:
   Rate at half = 10/2 = 5%, time doubles so t = 1 ½  = 3 hours
   So CI is Rs 1891.5
   Hence I > II 
3. If the cost price of an article is increased by 40% to make it as the market price of article,
   Quantity I: Selling price of article after allowing a discount of 20%, if the cost price is Rs 1,75,000
   Quantity II: The cost price of article if after selling  article at 20% profit is Rs 2,52,000
   A) Quantity I > Quantity II
   B) Quantity I ≥  Quantity II
   C) Quantity II > Quantity I
   D) Quantity II ≥  Quantity I
   E) Quantity I = Quantity II or Relation cannot be established
   
   View Answer

      Option C
   Solution:
   40% = 2/5 [CP  = 5, MP = 7] ………………..(1)
   I: discount = 20% = 1/5 [MP = 5, SP = 4] ………………(2)
   make MP same by multiplying (1) by 5 and (2) by 7
   CP………..SP…………MP is
   25………..28…………35
   So SP = 196000
   II: profit = 20% = 1/5 [CP = 5, SP = 6] ………………(3)
   CP is same, so from (3) and (1):
   CP………..SP…………MP is
   5………….6…………..7
   So CP = 210000
   Hence II > I 
4. Four years ago, the ratio of ages of A and B is 5 : 6 and five years after the ratio will become 6 : 7, then
   Quantity I: present age of A
   Quantity II: age of B 4 years ago
   A) Quantity I > Quantity II
   B) Quantity I ≥ Quantity II
   C) Quantity II > Quantity I
   D) Quantity II ≥  Quantity I
   E) Quantity I = Quantity II or Relation cannot be established
   
   View Answer

      Option C
   Solution:
   .                               A………..B
   4 years ago  ====   5…………6
   5 years hence ==     6…………7
   1 == 9 and 6 ==54
   5 == 45
   I: A’s present age = 45+4 = 49
   II: B’s age 4 years ago = 54
   Hence II > I 
5. Quantity I: The largest number if average of 5 consecutive odd numbers is 39.
   Quantity II: The smallest number if average of 5 consecutive of odd numbers is 47.
   A) Quantity I > Quantity II
   B) Quantity I ≥  Quantity II
   C) Quantity II > Quantity I
   D) Quantity II ≥  Quantity I
   E) Quantity I = Quantity II or Relation cannot be established
   
   View Answer

      Option E
   Solution:
   I: 35, 37, 39, 41,43
   II: 43, 45, 47, 49, 51
   So CSA = 2πrh = 528cm²
   Hence I = II 
6. Quantity I: Number of days required by A to complete work alone, if A and B together can complete work in 20 days. Given that after they start work together, A leaves work after 10 days and B completed the remaining work in 20 days.
   Quantity II: Number of days required by A to complete work alone, if A and B together can complete work in 15 days. Given that after they start work together, A leaves work after 5 days and B completed the remaining work in 30 days.
   A) Quantity I > Quantity II
   B) Quantity I ≥  Quantity II
   C) Quantity II > Quantity I
   D) Quantity II ≥  Quantity I
   E) Quantity I = Quantity II or Relation cannot be established
   
   View Answer

      Option A
   Solution:
   I: 1/20 * 10 + 1/B * 20 = 1
   B= 40
   So 1/A = 1/20 – 1/40
   So A in 40 days
   II: 1/15 * 5 + 1/B * 30 = 1
   B= 45
   So 1/A = 1/15 – 1/45
   So B in 22.5 days
   Hence I > II 
7. Quantity I: The length of train if train can cross a pole in 18 seconds and a 210 m platform in 39 seconds.
   Quantity II: The length of platform if 200 m long train passes a pole in 20 seconds and platform in 46 seconds
   A) Quantity I > Quantity II
   B) Quantity I ≥  Quantity II
   C) Quantity II > Quantity I
   D) Quantity II ≥  Quantity I
   E) Quantity I = Quantity II or Relation cannot be established
   
   View Answer

      Option C
   Solution:
   I: Train covers own length in 18 seconds and platform in 39 seconds. But in these 39 seconds it covered its own length also, so platform in 39-18 = 21 seconds
   Train => 18 ==180 m
   Platform => 21 == 210 m
   II: Same concept in I,
   Train => 20 == 200 m
   Platform => 26 == 260 m
   Hence II > I
8. Initial speed of bus is 60 km/hr
   Quantity I: the stoppage time if bus travels at 45 km/hr after stopping at a point
   Quantity II: the stoppage time if bus travels at 40 km/hr after stopping at a point
   A) Quantity I > Quantity II
   B) Quantity I ≥  Quantity II
   C) Quantity II > Quantity I
   D) Quantity II ≥  Quantity I
   E) Quantity I = Quantity II or Relation cannot be established
   
   View Answer

      Option C
   Solution:
   I: stoppage time = (initial – secondary)/initial * 60
   So (60-45)/60 * 60 = 15 min
   II: (60-40)/60 * 60 = 20 min
   Hence II > I 
9. Quantity I: Three successive discounts of 33 1/3%, 20% and 25%
   Quantity II: Three successive discounts of 16 2/3%, 14 2/7% and 12.5%
   A) Quantity I > Quantity II
   B) Quantity I ≥  Quantity II
   C) Quantity II > Quantity I
   D) Quantity II ≥  Quantity I
   E) Quantity I = Quantity II or Relation cannot be established
   
   View Answer

      Option A
   Solution:
   I:
   33 1/3% = 1/3 ……………………………3 -> 2
   20% = 1/5…………………………….…….5 -> 4
   25% = 1/4…………..……………………..4 -> 3
   
   Similarly in II:
   
   Hence I > II 
10. Quantity I: x, 5x² + 23x + 12 = 0
    Quantity II: y, 5y² – 7y – 6 = 0
    A) Quantity I > Quantity II
    B) Quantity I ≥  Quantity II
    C) Quantity II > Quantity I
    D) Quantity II ≥  Quantity I
    E) Quantity I = Quantity II or Relation cannot be established
    
    View Answer

       Option D
    Solution:
    5x² + 23x + 12 = 0
    5x² + 20x + 3x + 12 = 0
    So x = -4, -3/5
    5y² – 7y – 6 = 0
    5y² – 10y + 3y – 6 = 0
    So y = -3/5, 2
    Hence I ≤ II