Integers Test

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Integers Test - 6

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Weekly Quiz Competition

Question 1
1 / -0

Thevalue of $\frac{15 \times (- 24) \times - 18}{- (27) \times (20)}$ is

A
-16

B
-15

C
-12

D
12

Solution

Asthere are 22 negative numbers in the numerator and 11 in the denominator, theanswer will be negative.
Cancellingout the common factors and simplifying we get
$\frac{15 \times (- 24) \times - 18}{- (27) \times (20)} = \frac{3 \times 8 \times 18}{- 9 \times 4}$
= $- 3 \times 2 \times 2 = - 12$
Question 2
1 / -0

78×.......=−78

A
1

B
178

C
0

D
-1

Solution

78*(-1) = -78
Hence option d is correct.
Question 3
1 / -0

Simplifythe following:-
(−441)÷ (21) =?

A
21

B
-21

C
20

D
-20

Solution

$\frac{- 441}{21} = - 21$
Hence option b is correct.
Question 4
1 / -0

Multiply:
(−5) × 8 and 3 × (−2)

A
240

B
420

C
-240

D
-420

Solution

(−5) × 8 = −40
3 × (−2) = − 6
Hence, _{−5) × 8) × (3 × (−2} = −40 × −6 = 240
Question 5
1 / -0

−42 × x = 336, −28 × y = −84
What is the value of x and y respectively?

A
8and 3

B
−8and 3

C
8and −3

D
−8and −3

Solution

$G i v e n, - 42 \times x = 336 a n d - 28 \times y = - 84$
Thusx = $\frac{336}{- 42}$ =-8
and y = $\frac{- 84}{- 28}$ =3
Question 6
1 / -0

$- 32 \times x = 160, - 23 \times y = - 115$
What is the value of x ÷ y?

A
-1

B
1

C
-5

D
5

Solution

$G i v e n, - 32 \times x = 160, - 23 \times y = - 115 W e h a v e x = \frac{160}{- 32}$
andy= $\frac{- 115}{- 23} = \frac{115}{23}$
$T h u s \frac{x}{y} = \frac{160 \times 23}{- 32 \times 115} = - \frac{32 \times 23}{32 \times 23} = - 1$
Question 7
1 / -0

(−1)¹¹value is

A
+1

B
0

C
-1

D
None of these

Solution

We know that if the power n of any negative integer x iseven then the resulting integer will always be positive and if the power n ofany negative integer x is odd then the resulting integer will always benegative. For example, if the negative integer is x =−2, then
Odd power:
(−2)³ = −2 × −2 × −2 = −8 = which is a negativeinteger.
Even power:
(−2)²= −2 ×− 2 = 4 which is a positive integer.
Similarly, (−1)¹¹= −1 because −1 is a negativeinteger and 11 is an odd number, so the result will be a negative integer.
Hence, (−1)¹¹ = −1
Question 8
1 / -0

Which of the following pairs of integers have 19 as adifference?

A
29,10

B
-29,-10

C
19,-10

D
Bothe a and b

Solution

Thedifference between 29, 10 is |29−10|= 19, also the difference between −29,−10is |−29−(−10)|= 19.
Again the difference between 29, −10 is |29−(−10)|= 19.
So option (a) and (b) are true.
Question 9
1 / -0

Solve−132÷11

A
+101

B
-101

C
+11

D
-12

Solution

Wecan write −132 ÷ 11 as $- 132 \times \frac{1}{11}$
Or, $\frac{- 132}{11}$ =(-12)
So option D is the correct answer.
Question 10
1 / -0

Multiplicationof a negative integer for even times gives a _____result

A
Negative

B
0

C
Positive

D
None

Solution

Multiplication 2 times: (−2) × (−2)=4
Multiplication 4 times: (−3) × (−3) × (−3) × (−3)=9 × 9=81
Multiplication 6 times: (−1)×(−1)×(−1)×(−1)×(−1)×(−1)=1×1×1=1
Hence, when a negative integer is multiplied even number oftimes, the result is a positive integer.
Question 11
1 / -0

Findthe value of x in this equation: $\frac{392}{x} = - 196$

A
2

B
4

C
-2

D
-4

Solution

$\frac{392}{x} = - 196$
$\frac{392}{- 196} = x$
$x = - 2$
Question 12
1 / -0

Thetemperature at Bar Harbor, Maine, was −2^o F. It then dropped duringthe night to be 5 times as cold. What was the temperature then?

A
12^oF

B
−10^oF

C
16^oF

D
−16^oF

Solution

Since the temperature is 5 times as cold.
∴ Temperature then was 5 × −2 = −10^oF
Question 13
1 / -0

Themultiplicative inverse of 2⁻⁴ is

A
2

B
4

C
2⁴

D
-4

Solution

A reciprocal is a number obtained by interchanging numeratorand denominator. Multiplicative inverse means the same thing as reciprocal.
The product of a number and its multiplicative inverse is 1.
And, we have 2⁻⁴× 2⁴= 2⁴⁻⁴= 1
Thus, multiplicative inverse of 2⁻⁴ is2⁴
Question 14
1 / -0

Whatvalue should come in place of question mark (?) in the questions given below?
43 × 5 =?

A
215

B
220

C
20

D
251

Solution

43× 5 = 215
Question 15
1 / -0

(-12)× (-3) × (+4) × (-6) =

A
-144

B
-908

C
+864

D
-864

Solution

There are 3 negative signs. So, the resultant of 3multiplications would be negative.
∴ (−12) × (−3) × (+4)× (−6)= 36 × 4 × (−6)
⇒144 × (−6) = −864

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Integers Test - 6

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Integers Test - 6

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Question 1

-16

-15

-12

12

Solution

Question 2

1

178

0

-1

Solution

Question 3

21

-21

20

-20

Solution

Question 4

240

420

-240

-420

Solution

Question 5

8and 3

−8and 3

8and −3

−8and −3

Solution

Question 6

-1

1

-5

5

Solution

Question 7

+1

0

-1

None of these

Solution

Question 8

29,10

-29,-10

19,-10

Bothe a and b

Solution

Question 9

+101

-101

+11

-12

Solution

Question 10

Negative

0

Positive

None

Solution

Question 11

2

4

-2

-4

Solution

Question 12

12oF

−10oF

16oF

−16oF

Solution

12^oF

−10^oF

16^oF

−16^oF

2⁴