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Arithmetic Aptitude | Numbers IV - with Explanation


1. 
If (64)2 - (36)2 = 20 x x, then x = ?
A.70
B.120
C.180
D.140
E.None of these
Answer: Option D
Explanation:
20 x x = (64 + 36)(64 - 36) = 100 x 28
      x =100 x 28= 140
20


2. 
Which one of the following can't be the square of natural number ?
A.32761
B.81225
C.42437
D.20164
E.None of these
Answer: Option C
Explanation:
The square of a natural number never ends in 7.
42437 is not the square of a natural number.

3. 
(22 + 42 + 62 + ... + 202) = ?
A.770
B.1155
C.1540
D.385 x 385
Answer: Option C
Explanation:
(22 + 42 + 62 + ... + 202) = (1 x 2)2 + (2 x 2)2 + (2 x 3)2 + ... + (2 x 10)2
= (22 x 12) + (22 x 22) + (22 x 32) + ... + (22 x 102)
= 22 x [12 + 22 + 32 + ... + 102]
Ref: (12 + 22 + 32 + ... + n2) =1n(n + 1)(2n + 1)   
6
=4 x1x 10 x 11 x 21
6
= (4 x 5 x 77)
= 1540.

4. 
854 x 854 x 854 - 276 x 276 x 276= ?
854 x 854 + 854 x 276 + 276 x 276
A.1130
B.578
C.565
D.1156
E.None of these
Answer: Option B
Explanation:
Given Exp. =(a3 - b3)= (a - b) = (854 - 276) = 578
(a2 + ab + b2)


5. 
35 + 15 x 1.5 = ?
A.85
B.51.5
C.57.5
D.5.25
E.None of these
Answer: Option C
Explanation:
Given Exp. = 35 + 15 x3  = 35 +45  = 35 + 22.5   = 57.5
22


6. 
The sum of first 45 natural numbers is:
A.1035
B.1280
C.2070
D.2140
Answer: Option A
Explanation:
Let Sn = (1 + 2 + 3 + ... + 45)
This is an A.P. in which a = 1, d = 1, n = 45 and l = 45
Sn =n(a + l)=45x (1 + 45)   = (45 x 23)   = 1035
22
Required sum = 1035.

7. 
666 ÷ 6 ÷ 3 = ?
A.37
B.333
C.111
D.84
E.None of these
Answer: Option A
Explanation:
Given Exp. = 666 x1x1= 37
63


8. 
The sum of all two digit numbers divisible by 5 is:
A.1035
B.1245
C.1230
D.945
E.None of these
Answer: Option D
Explanation:
Required numbers are 10, 15, 20, 25, ..., 95
This is an A.P. in which a = 10, d = 5 and l = 95.
tn = 95        a + (n - 1)d = 95
 10 + (n - 1) x 5 = 95
 (n - 1) x 5 = 85
 (n - 1) = 17
 n = 18
Requuired Sum =n(a + l)=18x (10 + 95)   = (9 x 105)   = 945.
22


9. 
The difference between the place values of two sevens in the numeral 69758472 is
A.0
B.6993
C.699930
D.None of these
Answer: Option C
Explanation:
Required difference = (700000 - 70) = 699930

10. 
On dividing a number by 68, we get 269 as quotient and 0 as remainder. On dividing the same number by 67, what will the remainder ?
A.0
B.1
C.2
D.3
Answer: Option B
Explanation:
Number = 269 x 68 + 0 = 18292

 67) 18292 (273
     134
     ----
      489
      469
      ----
       202
       201
       ---
         1
       ---
       
Therefore, Required remainder = 1


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