1.
On dividing a number by 4, the sum of quotient and remainder is 8 and sum of their squares is 34. Find the number.
• A.
24
• C.
23
• B.
22
• D.
25
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Explanation :
Let the quotient be Q and remainder = R
Given, number = 4Q + R
 Q + R = 8 ------------ (1)
 Q2 + R2 = 34 ------------ (2)
(Q + R)2 = Q2 + R2 = 2QR
82 = 34 + 2QR    QR =
 64 - 34 2
= 15
(Q � R)2 = Q2 �+ R2 � 2QR = 34 � 30 = 4
 Q - R = 2 ------------ (3)
Adding (1) and (3) 2Q = 10   Q = 5
R = 8 - Q = 8 - 5 = 3
The number = 4Q + R = (4 x 5) + 3 = 20 + 3 = 23
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2.
In a forest, there are some rabbits and pigeons. They have 20 heads and 48 feet. How many pigeons are there?
• A.
8
• C.
6
• B.
16
• D.
4
• Report
Explanation :
Let x be the no. of rabbits and y be the no. of pigeons.
 Then, x + y = 20 ................ (1)
 4x + 2y = 48 ................ (2)
Solving (1) and (2) we get x = 4, y = 16
No. of. Pigeons = 16.
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3.
The sum of three numbers is 60. If the ratio between first and second is 1 : 2 and that between second and third is 2 : 3 then the second number is
• A.
30
• C.
15
• B.
10
• D.
20
• Report
Explanation :
 A : B = 1 : 2 and B : C = 2 : 3

A : B : C = 1 : 2 : 3
Second number =
 2 6
x 60 = 20
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4.
The difference between the numerator and denominator of a fraction is 5. If 5 is added to its
denominator the fraction is decreased by 1
 1 4
. Find the value of the fraction
•  A. 1 6
• B.
3  1 4

• B.
2  1 4

• D.
6
• Report
Explanation :
Let the denominator of the fraction be = x
Then, numerator = x + 5
 x + 5 x
-
 x + 5 x + 5
=
 5 4

 x + 5 x
=
 5 4
+ 1

 x + 5 x
=
 9 4
= 2
 1 4

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5.
When a teacher distributed craft papers to students in her class each one got 7 papers, and 14 papers remained with the teacher. If two more students would have been in the class, no paper would have remained undistributed. How many students, the teacher had in her class?
• A.
70
• C.
52
• B.
58
• D.