 ## Simplification problems

• 1.  (469 + 174)2 - (469 - 174)2 =? (469 x 174)

• Options
• A. 2
• B. 4
• C. 295
• D. 643
• 2. A man has Rs.480 in the denominations of one-rupee notes, five-rupee notes and ten-rupee notes. The number of notes of each denomination is equal. What is the total number of notes that he has?

• Options
• A. 45
• B. 60
• C. 75
• D. 90
• 3. There are two examinations rooms A and B. If 10 students are sent from A to B, then the number of students in each room is the same. If 20 candidates are sent from B to A, then the number of students in A is double the number of students in B. The number of students in room A is:

• Options
• A. 20
• B. 80
• C. 100
• D. 200
• 4. David gets on the elevator at the 11th floor of a building and rides up at the rate of 57 floors per minute. At the same time, Albert gets on an elevator at the 51st floor of the same building and rides down at the rate of 63 floors per minute. If they continue travelling at these rates, then at which floor will their paths cross?

• Options
• A. 19
• B. 28
• C. 30
• D. 37
• 5. A fires 5 shots to B's 3 but A kills only once in 3 shots while B kills once in 2 shots. When B has missed 27 times, A has killed:

• Options
• A. 30 birds
• B. 60 birds
• C. 72 birds
• D. 90 birds
• 6. One-third of Rahul's savings in National Savings Certificate is equal to one-half of his savings in Public Provident Fund. If he has Rs. 1,50,000 as total savings, how much has he saved in Public Provident Fund?

• Options
• A. Rs. 30,000
• B. Rs. 50,000
• C. Rs. 60,000
• D. Rs. 90,000
• 7. If a - b = 3 and a2 + b2 = 29, find the value of ab.

• Options
• A. 10
• B. 12
• C. 15
• D. 18
• 8. The price of 10 chairs is equal to that of 4 tables. The price of 15 chairs and 2 tables together is Rs. 4000. The total price of 12 chairs and 3 tables is:

• Options
• A. Rs. 3500
• B. Rs. 3750
• C. Rs. 3840
• D. Rs. 3900
• 9. Eight people are planning to share equally the cost of a rental car. If one person withdraws from the arrangement and the others share equally the entire cost of the car, then the share of each of the remaining persons increased by:

• Options
• A. 17
• B. 18
• C. 19
• D. 78
• 10. Free notebooks were distributed equally among children of a class. The number of notebooks each child got was one-eighth of the number of children. Had the number of children been half, each child would have got 16 notebooks. Total how many notebooks were distributed?

• Options
• A. 256
• B. 432
• C. 512
• D. 640
• E. None of these