Number System Test

Result

Number System Test - 4

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Weekly Quiz Competition

Question 1
2 / -0.83

The sum of 3 consecutive even number is 40 more than the average of these numbers. Which of the following is the 2 largest number ?

A
18

B
20

C
22

D
24

Solution

X+x+2+x+4 = 40+(x+x+2+x+4)/3
3x+6 = 40+ (3x+6)/3
(9x+18 –3x-6)/3= 40
6x + 12 = 120
X = 108/6 = 18
18+2 = 20
Question 2
2 / -0.83

The sum of 3 consecutive number is 1251, Find the largest even number ?

A
420

B
414

C
418

D
416

Solution

X+x+1+x+2 = 1251
3x+3 = 1251
X = 1248/3 = 416
X+2 = 416+2 = 418
Question 3
2 / -0.83

What is the least number that can be added to 7218 make it a perfect square ?

A
7

B
5

C
6

D
4

Solution

85*85 = 7225
Question 4
2 / -0.83

If a = -2 and b = -5 then find the value of a³ + b³ –a² + b² + 2a –3b

A
-98

B
-100

C
101

D
-101

Solution

a³ + b³ –a² + b² + 2a –3b
(-2)³ + (-5)³ –(-2)² + (-5)² + 2(-2) –3(-5) = -8 -125-4+25-4+15 = -101
Question 5
2 / -0.83

x+(1/x) = 2, then find the value of x + (-1/x)

A
2

B
1

C
0

D
3

Solution

X+(1/X) = 2 ;

(X^2+ 1)/ X = 2 ;

X^2+1 = 2X ;

X^2 - 2X + 1= 0 ;

By factorisation method ,

X = 1 ;

Now substitute X= 1 in X +(-1/X) ;

we get , 1 - 1/1 = 0 ;

Therefore , X = 0 ;
Question 6
2 / -0.83

The average of 7 consecutive number is n, if the next 2 number also included then the new average will be increased by ?

A
0

B
1

C
2

D
3

Solution

Avg of 7 no= (7+1)/2 = 8/2 = 4
Avg of 9 no = (9+1)/2 = 5
5- 4 = 1
Hence increased by 1
Question 7
2 / -0.83

When a positive number n is divided by 7 leaves the remainder 2, when 3n is divided by the same number, then the remainder is

A
4

B
5

C
6

D
8

Solution

N = 7+2 =9
3n = 27
27/7 = 6
Question 8
2 / -0.83

The number of prime factors of 510510

A
4

B
5

C
6

D
7

Solution

2*3*5*7*11*13*17 = 510510
Question 9
2 / -0.83

25% of a number is 2 time 65% of another number.Find the ratio of the second no to the first number ?

A
5:26

B
26:5

C
23:7

D
5:23

Solution

(a*25)/100 = b(2*65)/100
a*25 = b*130
a/b = 130/25 = 26/5
b:a = 5:26
Question 10
2 / -0.83

Which one cannot be the square of a natural number ?

A
2116

B
2304

C
2202

D
2209

Solution

Square number can never end in 2,7
Question 11
2 / -0.83

When a number is subtracted from the number 8,12 and 20, the remainders are in continued proportion, Find the number ?

A
3

B
4

C
2

D
6

Solution

8-x / 12 –x = 12-x /20 –x
(8-x)(20-x) = (12 –x)(12 –x)
160 –8x –20x + x² = 144 –12x –12x + x²
4x = 16
x = 4
Question 12
2 / -0.83

Sum of the three consecutive number is 1956. What is 23% of the highest number ?

A
150.19

B
105.19

C
159.50

D
150.50

Solution

X+x+1+x+2 = 1956
3x = 1956 –3 = 1953
X = 1953/3 = 651
X+3 = 653
23% of largest num = 23*653/100 = 150.19
Question 13
2 / -0.83

If the numerator of a fraction is increased by 100% and the denominator is increased by 200%. The resultant fraction is 1 (1/15), What was the original fraction ?

A
1(4/3)

B
1(5/3)

C
1(3/5)

D
1(3/2)

Solution

1(1/15) = 16/15
X+x/y+2y = 16/15
2x/3y = 16/15
x/y = (16*3) / (15*2) = 8/5 = 1(3/5)
Question 14
2 / -0.83

Which of the following number is divisible by 11 ?

A
29435417

B
29435477

C
57463822

D
57648317

Solution

(9+3+4+7) –(2+4+5+1) = 11
Question 15
2 / -0.83

The sum of square of 2 number is 1972 and the difference of their square is 620. Find the number ?

A
33,26

B
34,25

C
36,26

D
38,28

Solution

X² + y² = 1972
X² –y² = 620
Solve this
2x² = 2592
x = 1296
x = 36
y² = 1972 –1296
y² = 676
y = 26
Question 16
2 / -0.83

Product of one fourth of the number and 120% of another number is what % of the product of the original number ?

A
35%

B
23%

C
32%

D
30%

Solution

x/4 = one fourth of the no
120y/100 = another no = 6y/5
% = [(x/4 * 6y/5)*100] / xy
= 600/20 = 30%
Question 17
2 / -0.83

Find the 5 digit number, 5^th digit is one fourth of the 3^rd digit and one half of the 4^th digit. 3^rd digit is one half of the 1^st digit. 2^nd digit is 5 more than the 5^th digit.

A
12786

B
86421

C
46218

D
24675

Solution
Question 18
2 / -0.83

What is the no of zeroes at the end of the product of the no from1 to 100 ?

A
20

B
22

C
24

D
25

Solution

100/5 + 100/25 = 20+4 = 24
Question 19
2 / -0.83

x+y = 8 and x/y = 7 ,find y

A
1

B
2

C
3

D
5

Solution

7y+y = 4
8y = 8 Y = 1
Question 20
2 / -0.83

If three numbers are added in pairs, the sums equal to 11,16 and 23.Find the three numbers

A
8,6,16

B
9,2,14

C
9,5,14

D
7,2,8

Solution

X+y = 11 - (1)
Y+z = 16 - (2)
Z+x = 23 -(3)
Add (1), (2), and (3)
2(x + y + z) = 50
X+y+z = 25
X = 25 –16 = 9
y = 25 –23 = 2
z = 25 –11 = 14