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Algebra Test - 12

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Algebra Test - 12

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Weekly Quiz Competition

Question 1
1 / -0

The value of x which satisfies the equation = 4 is

A
16

B
32

C
64

D
9

E
None of these

Solution

= 4
Squaring both sides,
14 + = 16
= 2
x^1/5 = 2
x = 2⁵
i.e. x = 32
Question 2
1 / -0

Which of the following is the largest in value?
(4⁴)⁴, 444, 44⁴, 4⁴⁴

A
(4⁴)⁴

B

C
444

D
44⁴

E
None of these

Solution

(4⁴)⁴ = 4⁴^×⁴ = 4¹⁶

444 = 444
44⁴ = 44 × 44 × 44 × 44
Clearly (2) is the greatest of all.
Question 3
1 / -0

If x + y = a and xy = b, then the value of + is

A
a³ – 3ab

B

C

D
a³ + 3ab

E
None of these

Solution

= ,
i.e. + = = + 3...
= + 3..

=
Question 4
1 / -0

is equal to

A
3³

B
3²

C
3^r

D

E
None of these

Solution

The given expression can be written as = = = 3^r
Question 5
1 / -0

A boy was asked to write 2⁵. 9²but he wrote 2592. The numerical difference between the values of 2⁵.9² and 2592 is

A
0

B
1

C
2

D
3

E
None of these

Solution

2⁵ × 9² = 2592
So there is no difference between the value written and the correct value.
Question 6
1 / -0

If xy = 2 and x² + y² = 5, then =

A
0

B
5/2

C
1

D

E
None of these

Solution

Given:
xy = 2 ... (1)
and x² + y² = 5 ... (2)
On dividing 2by 1, we get

= =
Question 7
1 / -0

If x and y are related as 15x²y^-1 = 225x, then find x^-1 in terms of y.

A

B

C
15y

D

E
None of these

Solution

15x²y^-1 = 225x
y^-1 = =
=
=
x^-1 =
Question 8
1 / -0

When you interchange the digits of the number 13, the number increases by 18. How many other two-digit numbers increase by 18 when their digits are interchanged?

A
5

B
6

C
7

D
8

E
None of these

Solution

Let x and y are the two digits of the number.
According to the question,
10x + y - 10y - x = 18
9x - 9y = 18
x - y = 2
Now the required numbers which have difference of 18 between their digits on interchanging are: 13,
24, 35, 46, 57, 68, 79
6 more numbers satisfy the given condition.
Question 9
1 / -0

In an examination, pass marks are 33%. A candidate who gets 210 marks fails by 21 marks. The total marks in the examination are

A
500

B
600

C
700

D
800

E
None of these

Solution

Passing marks = 210 + 21 = 231
Let total marks = x
Now, according to question,
33% of x = 231
x = = 700
Question 10
1 / -0

In a group of children, each child gives a gift to every other. If the number of gifts is 272, find the number of children.

A
13

B
16

C
17

D
21

E
None of these

Solution

Let x be the number of children.
n (n - 1) = 272
n² - n - 272 = 0
n² - 17n + 16n - 272 = 0
n (n - 17) + 16 (n - 17) = 0
(n + 16) (n - 17) = 0
n = - 16, 17
Number of children = 17
Question 11
1 / -0

A number consists of two digits, the sum of the digits being 10. If 18 is subtracted from the number, digits are reversed. Find the number.

A
37

B
46

C
55

D
64

E
None of these

Solution

Let the digit at unit`s place = y
And the digit at ten`s place = x
Original number = 10x + y
When digits are reversed, number becomes = 10y + x
According to the conditions,
x + y = 10 …(i)
10x + y - 18 = 10y + x …(ii)
Equation (ii) reduces to
9x - 9y = 18
x - y = 2 …(iii)
Adding (i) & (iii), we get
2x = 12 x = 6
Put x = 6 in eqn. (iii); y = 4 Original number = 64.
Question 12
1 / -0

A bag contains 89 coins of 50 and 25 cents only. If the total worth of the coins is Rs. 28.50, find the number of coins of each kind.

A
72, 17

B
64, 25

C
54, 35

D
36, 50

E
None of these

Solution

Let number of 50 paise coins = x & number of 25 paise coins = y
x + y = 89 ... (i)
50x + 25y = 2850
2x + y = 114... (ii)
x + y = 89
2x + y = 114
- - -
- x = - 25
Put value of x in equation (i)
y = 89 - 25
y = 64
Question 13
1 / -0

Maria buys one clown fish and 3 guppies for Rs. 5. If she buys 2 clown fishes and 5 guppies for Rs. 9, find the price of 1 guppy.

A
Rs. 1

B
Rs. 2

C
Rs. 3

D
Rs. 4

E
None of these

Solution

Let c be price of clown fish and g be that of guppy. c + 3g = 5 ....(i) and 2c + 5g = 9....(ii)
Solving (i) and (ii), we get g = 1, c = 2
Question 14
1 / -0

Five years ago, the age of Alison was 35 years more than James. At present, Alison is 3 times as old as James. How old James will be 10 years from now?

A
15 years

B
17 years

C
23 years

D
27 years

E
None of these

Solution

Let present age of James = J
Let present age of Alison = A
Now, according to question,
A = 3J ………..(1)
A - 5 = J - 5 + 35 ……..…(2)
A - 5 = J + 30
A - J = 35
From (1) and (2)
3J - J = 35
2J = 35
J =
Age of James after 10 years = + 10 = = 27.
Question 15
1 / -0

Seema weighs 5/9 of her weight plus 20 kg. What is the actual weight of Seema?

A
36 kg

B
72 kg

C
27 kg

D
45 kg

E
None of these

Solution

Let Seema`s actual weight = x kg
Now, according to the question,
x = + 20
= 20
x = 45 kg
Question 16
1 / -0

If x + y = 1, find the value of x³ + y³ + 3xy.

A
0

B
1

C
2

D
6

E
None of these

Solution

(x + y)³ =x³+ y³+ 3xy(x + y) putting value
(1)³ = x³ + y³ + 3xy (1)
x³ + y³ + 3xy = 1
Question 17
1 / -0

Divide 17 into two parts so that the difference between squares of numbers is 119.

A
12, 5

B
11, 6

C
15, 2

D
13, 4

E
None of these

Solution

Let one number be x
And second number = 17 - x
According to the given condition
(x)² - (17 - x)² = 119
x² - (289 + x² - 34x) = 119
x² - 289 - x² + 34x - 119 = 0
34x - 408 = 0
34x = 408
x = = 12
One number = 12
Second number = 12 - 7 = 5. Answer: (1)
B) You might have been careless by not checking that the sum of 12 and 7 is 19.
C) You might have not known the square of 17.
D) You might have thought that end digit of square of 20 is 0 and when we subtract 1 from it, we get the last digit as 9. Answer: (1)
Question 18
1 / -0

The product of two consecutive odd numbers is 575. Find the sum of the numbers.

A
84

B
58

C
46

D
48

E
2

Solution

Let first odd number = n
Second odd number = n + 2
According to condition,
n (n + 2) = 575
n² + 2n - 575 = 0
n² + 25n - 23n - 575 = 0
n (n + 25) - 23 (n + 25) = 0
(n + 25) (n - 23) = 0
n = - 25 Rejected
1^st odd number = 23 Second odd number = 25. Sum = 23 + 25 = 48 Answer: (4)
1) You might have written the answer as 84 instead of 48 by inter changing the digits.
2) You might have written the sum of 23 and 25 as 58 wrongly.
3) You might have made some calculation mistakes while performing multiplication operations.
5) You might have read the statement incorrectly and taken the difference of numbers instead of sum of the numbers.
Question 19
1 / -0

A number consists of two digits, the sum of the digits being 10. If 18 is subtracted from the number, the digits are reversed. Find the number.

A
37

B
55

C
46

D
64

E
73

Solution

Let the digit at unit`s place be y and the digit at ten`s place be x
Original number = 10x + y
When digits are reversed the number becomes = 10y + x
According to the conditions,
x + y = 10 …(i)
10x + y - 18 = 10y + x …(ii)
Equation (ii) reduces to
9x - 9y = 18
x - y = 2 …(iii)
Adding (i) & (iii), we get
2x = 12 x = 6
Put x = 6 in equation (iii); y = 4
Original number = 64. Answer: (4)
Original number = 64. Answer: (4)
1) You might have guessed that the sum of 3 and 7 is 10, and 37 might be the answer, by checking first option only.
2) You might have selected 46 instead of 64 by mistake.
3) You might have tried to solve the sum by adding the digits of the number randomly.
Question 20
1 / -0

Solve the following equation for x.
2x² - 14x + 14 = - 10

A
x = 4, - 3

B
x = 3, - 4

C
x = 3, 4

D
x = - 4, - 3

E
x = 4, 5

Solution

2x² - 14x + 14 = - 10
2x² - 14x + 24 = 0
2x² - 8x - 6x + 24 = 0
2x(x - 4) - 6(x - 4) = 0
(2x - 6) (x - 4) = 0
x = 3, 4
Answer: (3)
Question 21
1 / -0

Maria buys one clown fish and 3 guppies for $5 and 2 clown fish and 5 guppies for $9. Find the price of 1 guppy.

A
$1

B
$2

C
$3

D
$4

E
$5

Solution

Let c be price of clown fish and g be that of guppy.
c + 3g = 5 …….(i) and 2c + 5g = 9…………(ii)
Solving (i) and (ii), we get g = 1, c = 2
Question 22
1 / -0

If = 2^y, then y is equal to

A
5

B
3

C

D

E
None of these

Solution

= 2^x
= 2^x 2^5/3 = 2^x
x = 5/3
Question 23
1 / -0

Find a and b if = a - b

A
a = 11 and b = 6

B
a = 6 and b = 11

C
a = 6 and b = 6

D
a = 11 and b = 11

E
None of these

Solution

11 - 6
Comparing with a - b, a = 11 and b = 6
Question 24
1 / -0

If 4ⁿ + 4^n-1 = 20, then the value of nⁿ is

A
1

B
4

C
16

D
84

E
None of these

Solution

4^x + 4^{x - 1}
4^x = 4² x = 2
x^X = 2² = 4
Question 25
1 / -0

Find the value of + +

A
13

B
27

C
103

D
207

E
None of these

Solution

+ + = + +
= 6² + 4³ + 3
= 36 + 64 + 3 = 103.

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