Solving Equations Involving Absolute Number

Q. A two digit number is such that the product of its digits is 18. When 63 is subtracted from the number, the digits interchange their places. Find the number.
[4 MARKS]

Q.

If x and y are positive real numbers, then which of the following is correct?

1. $x>y\Rightarrow -x>-y$

2. $x>y\Rightarrow -x<-y$

3. $x>y\Rightarrow \frac{1}{x}>\frac{1}{y}$

4. $x>y\Rightarrow \frac{1}{x}>\frac{-1}{y}$

Q. The ages of two persons differ by $16$ years. If $6$ years ago, the elder one be $3$ times as old as the younger one, find their present ages.

1. 15 years and 31 years
2. 14 years and 30 years
3. 12 years and 28 years
4. 10 years and 26 years

Q.

The value of x that satisfies $|x-1|=|x+3|$ is

1. 1

2. -1

3. 2

4. -2

Q.

The value of x for which $|x-2|+|x-8|=10$ is

1. 3, 7

2. 1, 9

3. 2, 8

4. 0, 10

Q.

If $|x-2|+|x-6|=3$ then the value of $x$ is

1. No value for x

2. $x\le 2$

3. $2<x<6$

4. $x\ge 6$

Q.

If (3a+2b) : (5a+3b) = 18 : 29, find a : b

1. 3:2

2. 4:3

3. 5:3

4. 1:1

Q.

Question 120

What's the error? Ramu evaluated the expression - 7 - (- 3) and came up with the answer - 10. What did Ramu do wrong?

Q. The value of ${\left\{2-3(2-3{)}^3\right\}}^3$is

(a) 5

(b) 125

(c) 1/5

(d) -125

Q. Simplify the following expressions:

(i) $\left(11+\sqrt{11}\right)\left(11-\sqrt{11}\right)$

(ii) $\left(5+\sqrt{7}\right)\left(5-\sqrt{7}\right)$

(iii) $\left(\sqrt{8}-\sqrt{2}\right)\left(\sqrt{8}+\sqrt{2}\right)$

(iv) $\left(3+\sqrt{3}\right)\left(3-\sqrt{3}\right)$

(v) $\left(\sqrt{5}-\sqrt{2}\right)\left(\sqrt{5}+\sqrt{2}\right)$

Q.

All possible values of x when |3x -4| = 11 are

1. $+5,\frac{7}{3}$

2. $-5,\frac{7}{3}$

3. $+5,-\frac{7}{3}$

4. $-5,-\frac{7}{3}$

Q.

The value of x for which $|x-3|+|x-4|=9$ is

1. 8, 1

2. -8, 1

3. 8, -1

4. -8, -1

Q. If x < 5 and y > 8, then find the value of |x - y|.

Q.

Question 21

Fill in the blanks to make each statement true:

Three consecutive numbers whose sum is 12 are ......................, ......................., and ........................

Q.

Question 5

The next number in the pattern -62, -37, -12 is ___.

(a) 25
(b) 13
(c) 0
(d) -13

Q.

Question 31

Fill in the blanks to make each statement true:

The denominator of a rational number is greater than the numerator by 10. If the numerator is increased by 1 and the denominator is decreased by 1, then expression for new denominator is ..............

Q.

The value of |-44 + 62| + |11| - |28| is

1. 1

2. 0

3. 59

4. - 21

Q.

The value of |-71| - |-23 + 57| - 22 is

1. 51

2. -127

3. 15

4. -15

Q.

If $|y-3|=|y+1|$ then the value of y is

1. 1

2. 2

3. 3

4. 4

Q.

If $|x-2|=|x-6|$ then the value of $x$ is

1. 2

2. 4

3. 3

4. 1

Q.

The value of |4| $\times$ |-5 $\times$ 4| $\times$ 2

1. 48

2. 82

3. -8

4. 160

Q.

If x < 3 and y > 7, then |x - y| is

1. <4

2. >4

3. =4

4. None

Q.

Four friends M, N, O and P are playing cards. M and N are partners. If P faces towards North and M faces towards West, then who faces towards South?

1. Data inadequate
2. O
3. M
4. N

Q.

Which of the following satisfies.

$|x+y|<|x|+|y|$

1. x = 5, y = 2

2. x = -5, y = 3

3. x = 5, y = -2

4. x = -2, y = -5

Q.

The value of x for which 3| x + 2| = 18 is

1. $x=+4,+8$

2. $x=-4,+8$

3. $x=+4,-8$

4. $x=-4,-8$

Q.

If x < 3 & y > 7, then $|x-y|$ is

1. >5

2. <4

3. >4

4. >3

Q. A is twice as old as B. Ten years ago, A was four times as old as B. What are their present ages?

1. 24 and 12
2. 30 and 15
3. 32 and 16
4. 20 and 10

Q. The number $7490xy$ is divisible by $90$. Find out the value of $(x+y)$.

1. $4$
2. $5$
3. $6$
4. $7$

Q. The sum of two consecutive numbers is $37$. Find the numbers.

Q.

The value of x that satisfies $|x-1|=|x-3|$ is

1. 2

2. 3

3. 4

4. None