Important Quant Quiz On Simplification

1. If p – q = 6 and p^2 + q^2 = 116, what is the value of pq?
A. 30
B. 40
C. 20
D. 50

2.The price of 2 sarees and 4 shirts is Rs. 1600. With the same money one can buy 1 saree and 6 shirts. If one wants to buy 12 shirts, how much shall he have to pay ?

A. Rs. 1200
B. Rs. 2400
C. Rs. 4800
D. Cannot be determined
 3. If  a^2+b^2+c^2= 2(a-b-c)-3, then find the value of  2a-3b+4c.
A. 3
B. 1
C. 2
D. 4
4. To fill a tank, 25 buckets of water is required. How many buckets of water will be required to fill the same tank if the capacity of the bucket is reduced to three-fifth of its present?
A. 63
B. 64.5
C. 62.5
D. 60.5
5.A sum of Rs. 1360 has been divided among A, B and C such that A gets  2/3 of what B gets  and B gets 1/4 of what C gets. B’s share is:
A. Rs. 120
B. Rs. 160
C. Rs. 240
D. Rs. 300
 6.A man has Rs. 312 in the denominations of one-rupee notes, five-rupee notes and twenty-rupee notes. The number of notes of each denomination is equal. What is the total number of notes that he has ?
A. 36
B. 24
C. 28
D. 32
7.Simplfy  b – [b -(a+b) – {b – (b – a+b)} + 2a]
A. a
B. 2a
C. 4a
D. 0
8.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?
A. 602
B. 528
C. 423
D. 512
 9 .a * b = 2a – 3b + ab, then 3*5 + 5*3 = ?
A. 20
B. 21
C. 22
D. 23
10.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. 1,80,000 as total savings, how much has he saved in Public Provident Fund?
A. Rs. 72000
B. Rs. 44000
C. Rs. 58000
D. Rs. 92000

Note : Solution will be provided within an hour. you can give your answer in comment section.
ANSWER AND SOLUTION:

1(B)Explanation :
(a-b)^2=a^2-2ab+b^2
so (p – q)^2 = p^2 – 2pq + q^2
(p – q)^2 = (p^2 + q^2)- 2pq
6^2 = 116 – 2pq
36 = 116 – 2pq
2pq = 80
pq = 40

2(B)Explanation:
Let the price of a saree and a shirt be Rs. x and Rs. y respectively.
Then, 2x + 4y = 1600 …. (i)
    and x + 6y = 1600 …. (ii)
Divide equation (i) by 2, we get the below equation.
=> x +  2y =  800. — (iii)
Now subtract (iii) from (ii)
 x +  6y = 1600  (-)
 x +  2y =  800
—————-
      4y =  800
—————-
Therefore, y = 200.
Now apply value of y in (iii)
=>  x + 2 x 200 = 800
=>  x + 400 = 800
Therefore x = 400
Solving (i) and (ii) we get x = 400, y = 200.
so  Cost of 12 shirts = Rs. (12 x 200) = Rs. 2400.

3(B)Explanation:
a^2 + b^2+c^2 = 2(a-b-c)-3
a^2 + b^2+c^2-2(a-b-c)+3=0
a^2 + b^2+c^2-2a+2b+2c+1+1+1=0
(a^2+1-2a)+ (b^2+1+2b)+(c^2+1+2c)= 0
(a-1)^2+(b+1)^2+(c+1)^2= 0
so a = 1, b = -1, c = -1
so 2a – 3b + 4c = 2×1 – ((3x(-1)) + 4x(-1)
                  = 2 +3 – 4
                  = 5 – 4
                  = 1

4(C)Explanation :
Let x buckets of water be required ,if the capacity of the bucket is reduced to two-fifth
More buckets, less capacity (Indirect proportion)
Hence we can write as
Capacity  1 : 2/5 } :: x : 25
1×25 = 2/5×x
25 = 2x/5
x=25×5/2 = 62.5
i.e., 62.5 buckets are needed

5(C)Explanation:
Let C’s share = Rs. x
Then, B’s share = Rs. x/4 ,   A’s share = Rs.(2/3 x x/4) = Rs. x/6
so, x/6 + x/4 + x = 1360
=>17x/12 = 1360
=>  x =1360 x 12/17 = Rs. 960
Hence, B’s share = Rs. (960/4) = Rs. 240.

6( A)Explanation :
Let the number of notes of each denomination be x
Then, x + 5x + 20x = 312
=> 26x = 312
=> x = 312/26 = 12
the total number of notes that he has = 3x = 3 × 12 = 36

 7(D)Explanation:
b-[b-(a+b)-{b-(b-a+b)}+2a]
=b-[b-a-b-{b-(2b-a)}+2a]
=b-[-a-{b-2b+a}+2a]
=b-[-a-{-b+a}+2a]
=b-[-a+b-a+2a]
=b-[-2a+b+2a]
=b-b
=0

8(D)Explanation :
Let n be the total number of children.
More children, less notebooks(Indirect proportion)
If the number children = n, number of books each child will get =  n/8
If the number children = n/2, number of books each child will get = 16
Hence we can write as
children  n : n/2 } :: 16 : n/8
n×n/8 = n/2×16
n/8 = 16/2 = 8
n = 8×8 = 64
Then, total number of notebooks those were distributed = n×n/8 = 64×64/8 = 64×8=512

9(C)Explanation:
= 2(3)-3(5)+(3*5) + 2(5)-3(3)+(5*3)
= 6-15+15+10-9+15 = 31-9 = 22

10(A)Explanation :
Let savings in National Savings Certificate = x
and savings in Public Provident Fund = (180000 – x)
1/3 x = 1/2(180000-x)
2x = 3(180000-x)
2x = 540000-3x
5x = 540000
x=540000/5 = 108000
Savings in Public Provident Fund = (180000 – 108000) = 72000

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