Simplify 1.53 + 4.73 + | Simplification Questions & Answers

Q:

Hemavathi gets 3 marks for each right sum and loses 2 marks for each wrong sum. He attempts 35 sums and obtains 60 marks. The number of sums attempted correctly is ?

A) 23	B) 24
C) 25	D) 26

Answer & Explanation Answer: D) 26

Explanation:

Let, Hema attempted 'k' sum correctly, then

k x 3 -2 x(35-k) = 60
5k = 130
k = 26

so 26 correct sums.

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9 6360

Q:

The average temperature of Monday to Wednesday was 37 C and of Tuesday to Thursday was 34 C. If the temperature on Thursday was 4/5 th of that of Monday, the temperature on Thursday was ?

A) 35 c	B) 36 c
C) 34 c	D) 32 c

Answer & Explanation Answer: B) 36 c

Explanation:

Monday + Tuesday + Wednesday = 37 x 3 -----------(1)
Tuesday + Wednesday + Thursday = 34 x 3---------(2)
Thursday = 4/5 of Monday ------------------(3)
subtract eqn (1) from (2) we get,
Thursday - Monday = -9
=> Monday - Thursday = 9.......(4)
From (3) & (4), we get

So,Thursday = 36 C

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3 3655

Q:

A secret can be told to only 3 persons in 3 minutes. Each person in turn tells 3 other persons in the next 3 minutes and the processes continues accordingly. In 30 minutes how many persons can be told this secret in this way ?

A) 88572	B) 77854
C) 99584	D) 55654

Answer & Explanation Answer: A) 88572

Explanation:

Given a secret is told to 3 persons in 3 minutes.
And if the process continues with each person saying 3 other persons,
In 30 minutes => the rocess for 10 times because each person time is 3 minutes.
Required number of persons = $3 + 3^{2} + 3^{3} + . . . . + 3^{9} + 3^{10}$

Now it forms a geometric progression,

Sum to n terms is $S = \frac{a (r^{n} - 1)}{r - 1}$

Here a = 3, r = 3

=> 59048 x 3 /2

= 88572.

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5 3756

Q:

In a party there are male and female members. If 15 female quit then the number of females will become double the number of males. If 45 males quit no. of female becomes five times the number of males. Find the number of females ?

A) 175	B) 145
C) 165	D) 135

Answer & Explanation Answer: A) 175

Explanation:

Let the number of males be 'M'
Let the number of females be 'F'
From the given conditions,
(F-15)=2M.....(i)
F=5(M-45).....(ii)
By solving the equations (1) & (2) we get M = 80
Then substitute M = 80 in (1)
F = 2M + 15
F = 2 x 80 + 15
=> F = 175
Therefore, number of males = 80 and females = 175 in the party.

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5 2900

Q:

A class consists of both boys and girls along with a teacher. After a class, the teacher drinks 9 litres of water, a boy drinks 7 litres of water and a girl drinks 4 litres of water. If after a class 42 litres of water was consumed, find the number of girls in the class ?

A) 8	B) 6
C) 5	D) 3

Answer & Explanation Answer: D) 3

Explanation:

Given teacher drinks 9 ltr
Let number of boys be 'A'.
Let number of girls be 'B'.
Boy drinks 7 ltr and girl drinks 4 ltr
After class total water consumed = 42 ltr
Then,
9 + 7A + 4B = 42
=> 7A + 4B = 33
By trial and error method,
The only integers which satisfy the equation is A = 3 and B = 3
Therefore, number of girls in the class = 3.

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6 3123

Q:

The average number of visitors of a library in the first 4 days of a week was 58. The average for the 2nd, 3rd, 4th and 5th days was 60.If the number of visitors on the 1st and 5th days were in the ratio 8 : 9. Then what is the number of visitors on the 5th day of the library ?

A) 54	B) 64
C) 68	D) 72

Answer & Explanation Answer: D) 72

Explanation:

If number of visitors on 1st, 2nd, 3rd, 4th & 5th day are k, l, m, n & o respectively, then
k + l + m + n = 58 x 4 = 232 ---- (i) &
l + m + n + o = 60 x 4 = 240 ---- (ii)
Subtracting (i) from (ii), we get
o-k = 8 ---(iii)
Given, k/o = 8/9 ----(iv)
So from (iii) & (iv), we get
a = 64, e = 72
Therefore, number of visitors on 5th day is 72.

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8 6594

Q:

5 sin(x)+ 12 cos(x) + r is always greater than or equal to zero. What is the smallest value satisfied by 'r' ?

A) -13	B) 11
C) 13	D) -11

Answer & Explanation Answer: C) 13

Explanation:

Given,

5sinx + 12cosx ≥ -r

$\Rightarrow 13 (\frac{5}{13} \sin x + \frac{12}{13} \cos x) \geq - r$ cosx) ≥ -r

$\frac{5}{13}$ = cosA => sinA = $\frac{12}{13}$

=> 13(sinx cosA + sinA cosx) ≥ -r

=> 13(sin(x + A)) ≥ -r

we know that , -1 ≤ sin (angle) ≤ 1

=> 13sin (x + A) ≥ -13 $\Rightarrow r_{m i n} = 13$

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8 4855

Q:

If $3^{x - y} = 27$ , $3^{x + y} = 243$ then find the x value

A) 2	B) 8
C) 4	D) 1

Answer & Explanation Answer: C) 4

Explanation:

Given that $3^{x - y} = 27$ , $3^{x + y} = 243$

$\Rightarrow 3^{x - y} = 3^{3}, 3^{x + y} = 3^{5}$

=> x-y=3, x+y=5

=> x = 4

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15 9787

A) 6	B) 8
C) 10	D) 12

Simplify

$\frac{1 . 5^{3} + 4 . 7^{3} + 3 . 8^{3} - 3 x 1.5 x 4.7 x 3.8}{1 . 5^{2} + 4 . 7^{2} + 3 . 8^{2} - 1.5 x 4.7 - 4.7 x 3.8 - 1.5 x 3.8}$

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Simplify 1.53 + 4.73 + 3.83 - 3 x 1.5 x 4.7 x 3.81.52 + 4.72 + 3.82 - 1.5 x 4.7 - 4.7 x 3.8 - 1.5 x 3.8

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Simplify

$\frac{1 . 5^{3} + 4 . 7^{3} + 3 . 8^{3} - 3 x 1.5 x 4.7 x 3.8}{1 . 5^{2} + 4 . 7^{2} + 3 . 8^{2} - 1.5 x 4.7 - 4.7 x 3.8 - 1.5 x 3.8}$