Inequalities Test

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Inequalities Test - 5

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Question 1
2 / -0.83

In drilling world’s deepest hole, it was found that the temperature T in degree Celsius, x km below the surface of Earth, was given by T = 30 + 25 (x – 3), 3 < x < 15. If the required temperature lies between 200^o C and 300^o C, then the depth, x will lie between

A
9 km and 13 km

B
9.8 km and 13.8 km

C
9.5 km and 13.5 km

D
10 km and 14 km

Solution

T = 30 + 25 (x – 3), 3 < x < 15
It is given 200 < T < 300
200 < 30 + 25 (x – 3) < 300
170 < 25(x - 3) < 270
170/25 (x - 3) < 270/25
6.8 + 3 < x < 10.8 + 3
9.8 < x < 13.8
Question 2
2 / -0.83

A solution of 10% boric acid is to be diluted by adding a 4% boric acid solution to it. The resulting mixture is to be more than 5% but less than 8% boric acid. If we have 750 litres of the 10% solution, then the quantity of the 4% solution that has to be added will lie between

A
370 litres and 3750 litres

B
375 litres and 3750 litres

C
320 litres and 1280 litres

D
370 litres and 3700 litres

Solution

Let x litres of 4% boric acid solution is required to be added
Then, total mixture = (x + 750)litres
This resulting mixture is to be more than 5% but less than 8% boric acid
Total amount of acid = 750 of 10% + x of 4%
ATQ
5/100(750 + x) <(750*10 + 4x)/100 <8/100(750 + x)
3750 + 5x <7500 + 4x ; 7500 + 4x <6000 + 8x
x <3750 ; x >375
375 and 3750
Question 3
2 / -0.83

Pairs of consecutive even positive integers, both of which are larger than 7 such that their sum is less than 28, are

A
(8, 9), (9, 10), (10, 11)

B
(8, 10), (10, 12)

C
(8, 10), (10, 12), (12, 14)

D
(8, 10), (10, 12), (12, 14), (14, 16)

Solution

Let x be the smaller of the two consecutive even positive integers .
Then the other integer is x+2.
Since both the integers are larger than 7,x >7 ....(1)
Also the sum of the two integers is less than 28.
x + (x + 2) <28
⇒2x + 2 <28
⇒2x <28 −2
⇒2x <26
=>x <13 …...(2)
From(1) and (2), we get
7 Since x is an even number, x can take the values 8, 10 and 12.
Thus the required possible pairs are (8,10),(10,12) and (12,8).
Question 4
2 / -0.83

The longest side of a triangle is 4 times the shortest side and the third side is 4 cm shorter than the longest side. If the perimeter of the triangle is at least 59 cm, then the minimum length of the shortest side is

A
9 cm

B
8 cm

C
7 cm

D
6 cm
Question 5
2 / -0.83

In an experiment a solution of hydrochloric acid is to be kept between 30 and 35 degree celcius. What is the range of temperature in degree Fahrenheit if conversion formula is given by ,where C and F represent temperature in degree celsius and degree fahrenheit, respectively?

A
30

B
86

C
62

D
77

Solution

Temperature is defined as the degree of hotness.
Temperature is measured using different scales in different regions.
we know that
C = temperature in celcius.
F = temperature in Fahrenheit.
F= 9(C)/5 + 32
1) C = 30
F= 9(30)/5 + 32
F= 54 + 32 = 86F
2) C = 35
F= 9(35)/5 + 32
F= 63 + 32 = 95F
The range of temperatures in degree Fahrenheit is 86 F to 95 F.
Question 6
2 / -0.83

A man wants to cut three lengths from a single piece of board of length 91 cm. The second length is to be 6 cm longer than the shortest and the third length is to be thrice as long as the shortest. If the third piece is to be at least 4 cm longer than the second, then the length of the shortest board will lie between

A
8 cm and 22 cm

B
6 cm and 19 cm

C
7 cm and 21 cm

D
5 cm and 17 cm

Solution

Let the length of the shortest piece, The length of the second price is (x+6)cm. The length of the third piece is 3x cm, Total length of the three prieces must be ≤91cm.
xcm+(x+6)cm+3xcm ≤91cm
=>5x+6 ≤91
Subtracting 6 from number 5 on both sides, 5x/5 ≤85/5
x ≤17----(1)
Step 2:
Also third piece is at least 4 cm longer than the second piece. therefore
3x ≥(x+6)+4
=>3x ≥x+10
Subtracting x from both sides,
3x −x ≥10
x ≥5 -----(2)
Step 3:
From (1) and (2)
5 ≤x ≤17
Question 7
2 / -0.83

A plumber can be paid under two schemes as given below:
I: Rs 600 and Rs 50 per hour.
II: Rs 170 per hour.
If the job takes n hours, then the values of n for which the scheme I will give the plumber better wages are

A
less than 4 hours

B
less than 5 hours

C
more than 5 hours

D
4 hours

Solution

Your question is not complete it should be,
I: &600 fix and &50 per hourNow solving the question,Let the work is done in n hour as per given , So After n hour according to first scheme he will get an amount
= 600+50n After n hour according to second scheme he will get an amount,
=170nNow we are asked for values of n such that scheme
I give better wages so 600+50n >170n600 >120nor n <5 .SO if the numbers of hour are less than 5 then he will get better wages by first scheme.
Question 8
2 / -0.83

In the first four examinations, each of 100 marks, Dipika got 94, 73, 72, 84 marks. If a final average greater than or equal to 80 and less than 90 is needed to obtain a final grade B in a course, then the range of marks, Dipika must score in the fifth examination in order to obtain grade B is

A
77 < x < 127

B
77 < x < 100

C
77 ≤ x < 127

D
77 ≤ x < 100

Solution
Question 9
2 / -0.83

The cost and revenue functions of a product are given by C(x) = 2x + 400 and R(x) = 6x + 20 respectively, where x is the number of items produced by the manufacturer. The minimum number of items that the manufacturer must sell to realize some profit is

A
95

B
96

C
105

D
100

Solution

Profit = revenue - cost
But given profit >0
therefore R(x) - C(x) >0
therefore 4x - 380 >0
therefore 4x >380
therefore x >95 manufacturer must sell 96 items.
Question 10
2 / -0.83

IQ of a person is given by the formula , where M A is mental age and CA is chronological age. If 85 < IQ < 145 for a group of 12-year children, then the mental age will lie between

A
10.4 and 17.2

B
10 and 18

C
10 and 17

D
10.2 and 17.4

Solution

85 ≤MA/CA ×100 ≤145
(85*12)/100 ≤MA/CA ×100 ≤(145*12)/100
10.2 ≤MA ≤17.4
range of mental age is[10.2,17.4].

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Inequalities Test - 5

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Inequalities Test - 5

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SHARING IS CARING

Question 1

9 km and 13 km

9.8 km and 13.8 km

9.5 km and 13.5 km

10 km and 14 km

Solution

Question 2

370 litres and 3750 litres

375 litres and 3750 litres

320 litres and 1280 litres

370 litres and 3700 litres

Solution

Question 3

(8, 9), (9, 10), (10, 11)

(8, 10), (10, 12)

(8, 10), (10, 12), (12, 14)

(8, 10), (10, 12), (12, 14), (14, 16)

Solution

Question 4

9 cm

8 cm

7 cm

6 cm

Question 5

30

86

62

77

Solution

Question 6

8 cm and 22 cm

6 cm and 19 cm

7 cm and 21 cm

5 cm and 17 cm

Solution

Question 7

less than 4 hours

less than 5 hours

more than 5 hours

4 hours

Solution

Question 8

77 < x < 127

77 < x < 100

77 ≤ x < 127

77 ≤ x < 100

Solution

Question 9

95

96

105

100

Solution

Question 10

10.4 and 17.2

10 and 18

10 and 17

10.2 and 17.4

Solution

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