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Problem Solving

Level 1 Questions
     

1. If p is a prime number greater than 2, which of the following is an even number?
 
      1.  2p + 1
      2.  p(p+2)
      3.  
      4.  (p - 1) (p + 1)
      5.  (p - 2) (p + 2)
 
Answer : 4
 
Explanation :
 
In option 4 both numbers in product are even so resulting number also should be even. In all other options both numbers in product are odd, so resulting number should also be odd.
 
2.  

B is the mid point of AC. What are the co-ordinates of C?
 
      1.  (-4,1)
      2.  (-4,-2)
      3.  (-4,-7)
      4.  (14,7)
      5.  (14,-7)
 
Answer : 5
 
Explanation :
 
The mid point of (x,y) and (x',y') is ((x+x')/2, (y+y')/2). Let C be the point (x, y). Then (x+(-4))/2 =5, (y+3)/2=-2 implies x=14, y=-7. Therefore C=(14, -7).

3. If P, Q and R are consecutive odd numbers in increasing order, what is (2R-(P+Q))/(R-Q)
 
      1.  0
      2.  3
      3.  2
      4.  4
      5.  Cannot be determined from information given

Answer : 2
 
Explanation :
 
Q=P+2, R=P+4. 2R-(P+Q)=2P+8-P-P-2=6 and R-Q=P+4-P-2=2. Therefore (2R-(P+Q))/(R-Q) = 3.
 
4.  
 
If the product of two numbers is 10 and the sum is 7, then the larger of the two numbers is
 
      1.  -2
      2.  +2
      3.  3
      4.  
      5.  5
 
Answer : 5
 
Explanation :
 
xy=10 implies x=(10/y). x+y=(10/y)+y=7. By solving above equation we get y=2 and x=5 or y=5 and x=2. In both cases larger one is 5.

5.  
A vessel which is full contains 4/7 water and 3/7 milk . Another vessel which is full has 16 litres of water and 12 litres of milk. A third vessel which is full has milk and water in the ratio 4 4/5 : 3 3/5 . If all three vessels are emptied onto a fourth vessel, what would be the ratio of water to milk in it?

      1.  5:3
      2.  4:3
      3.  12:13
      4.  4:1
      5.  1:4

Answer : 2

Explanation :

The ratios of the water and milk in the given three vessels are respectively (4/7):(3/7)=4:3,16:12=4:3 and 4 4/5 : 3 3/5 =(24/5):(18/5) =24:18 =4:3. Since all three vessels contain milk and water in the same ratio 4:3, the fourth vessel also will contain milk and water in the ratio 4:3 only.
 
6. A rectangle and a square have equal areas. However the length of the rectangle is thrice to the side of the square and the width is 4 inches less than the side of the square. What is the area of the rectangle?
 
      1.  12
      2.  25
      3.  36
      4.  48
      5.  49
 
Answer : 3
 
Explanation :
 
Let the side of the square be x. Then (x.x)=(3x)(x-4) implies 2x.x-12x=0 implies 2x(x-6)=0 implies x=6. (x is not equal 0 since it is a measure of a side of the square.) Therfore area of the square is 36.

7.  If ab=36 and = 25, find a and b ?
 
      1.  9 and 4
      2.  12 and 3
      3.   36 and 1
      4.  2 and 18
      5.   6 and 6
 
Answer : 1
 
Explanation :
 
From back substitution we can see only 9 and 4 satisfy the given equations.

8.  If (a, b) + (c, d) = (ac-bd,ad) then (-2, 3)+(4, -1)=
 
      1.  (-5, 2)
      2.  (5,2)
      3.  (-11, 2)
      4.  (-5, -2)
      5.  (5,-2)
 
Answer : 1
 
Explanation :

(-2, 3)+(4, -1)=((-2)(4)-(3)(-1)), (-2)(-1)) = (-8+3, 2)=(-5, 2).

9.  If the each side of a square is increased by 40%, then the increase in the area of the square will be
 
      1.  16%
      2.  40%
      3.  96%
      4.  116%
      5.  140%
 
Answer : 3
 
Explanation :
 
Let the side of the square be x. Then the area of the square will be is . After 40% increase the side becomes x+(40/100)x=(1.4)x. The area becomes 1.96. That is the area will increase by 0.96 times to the original area of the square. Therefore the increase of the area of the square in percentage will be 96%.

10. The expression (x+5) (3x-2) is equivalent to which of the following? i) x (3x-2) + 5 (3x-2) ii) 3x(x+5)+2(x+5) iii) x(3x-2)-2(x+5)
 
      1.  i only
      2.  ii only
      3.  iii only
      4.  i and ii
      5.  i, ii, iii
 
Answer : 1
 
Explanation :
 
After expansion the expression (x+5) (3x-2) we can see it is equivalent to i only.




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