Olympiad Test: Mathematical Reasoning - 1


15 Questions MCQ Test Mathematics Olympiad Class 7 | Olympiad Test: Mathematical Reasoning - 1


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Attempt Olympiad Test: Mathematical Reasoning - 1 | 15 questions in 30 minutes | Mock test for Class 7 preparation | Free important questions MCQ to study Mathematics Olympiad Class 7 for Class 7 Exam | Download free PDF with solutions
QUESTION: 1

Ravi got twice as many sums wrong as he got correct. If he attempted 96 sums in all. How many sums did he solve correctly.

Solution:

Let Ravi gets x sums correct.
∴ Wrong sums = 2x
Now x  + 2x = 96 ⇒ 3x = 96.

QUESTION: 2

In the numbers from 1 to 100, how many times 7 occurs?

Solution:

From 1 to 100, there are ten numbers with 7 as unit’s digit –
7, 17, 27, 37, 47, 57, 67, 77, 87,97.
And ten number with 7 as ten’s digit –
70, 71, 72, 73,74, 75, 76, 77, 78, 79. 
Required number = 10 + 10 = 20

QUESTION: 3

If 100 workers can finish a work in 100 days. then 40 workers can finish the work in how many days?

Solution:

∵ 100 workers finish a work in 100 days 
∴ 1 worker finish a work in 100 × 100
∴ 40 workers finish a work = 
= 250 days

QUESTION: 4

A number of students decided to go on a picnic and decided to spendRs. 96 on eatables. Four of them did not turn up, after that the remaining once had to contribute Rs. 4 each extra. What was the number of students in starting?

Solution:


⇒ x2 + 4x – 96 = 0
⇒ x2 + 12x – 8x – 96 = 0
⇒ x(x + 12) – 8 (x + 12) = 0
⇒ (x – 8) (x + 12) = 0 ( ∵x ≠ – 12) 
⇒ x – 8 = 0 ⇒ x = 8

QUESTION: 5

A bus starts from city A. the number of women in the bus is half of the number of men. In city B, 10 men leaves the bus and 5 women enters. Now number of men and women is equal. What is the number of passengers in the beginning?

Solution:

Let the number of women = x
Then number of men = 2x
In city B,
2x – 10 = x + 5 
⇒ 2x – x = 5 + 10 
⇒ x = 15
Total number of passengers in the beginning
= x  + 2x = 3x = 3 × 15 = 45 

QUESTION: 6

What is the smallest number of ducks that can swim in the way such that two ducks to front of a duck, two ducks behind a duck and a duck between two ducks?

Solution:


Smallest no. of ducks = 3 

QUESTION: 7

If a clock takes seven seconds to strike seven. How long will it take to strike 10?

Solution:

Seven strike of ducks = 3 intervals.
10 strikes have 9 intervals.
∵ 6 intervals have 7 sec and
∴ 1 interval have 7/6 second
∴ 9 intervals have 

QUESTION: 8

The total present age of Mihir, Sonu and Ritesh is 86 years. What will be the total age of these three persons after 2 years?

Solution:

Total ages of three persons = 86 years
Total ages of three persons after 2 years
= 86 + 2 + 2 + 2
= 92 years 

QUESTION: 9

In a caravan, in addition to 50 hens, there are 45 goats and 8 camels with some keepers. If the total number of feet be 224 more than the number of heads in the caravan, what is the number of keepers?

Solution:

Let the number of keepers be x.
A/Q, Total number of feet
= total no. of heads + 224
⇒ 50 × 2 + 45 × 4 + 8 × 4 + 2 × x
= 50 + 45 + 8 + x + 224
⇒ 100 + 180 + 32 + 2x = 327 + x
⇒ 312 + 2x = 327 + x
⇒ 2x – x = 327 – 312 
⇒ x = 15 

QUESTION: 10

Out of 450 students, 270 students passed. What is the percentage of students who did not pass?

Solution:

Number of students who did not pass
= 450 – 270 = 180

QUESTION: 11

What is that number which when added to itself 13 times, gives 112?

Solution:

Here,  x + 13x = 112

QUESTION: 12

In a family, each daughter has the same number of brothers as she has sisters and each son has twice as many sisters as he has brothers. How many sons are there in the family?

Solution:

Let d be the daughter and s be the son.
d – 1 = s ⇒ d – s = 1 ….(1)
2 (s – 1) = d ⇒ 2s – d = 2 …..(2)
From (1) and (2)
– s  + d = 1
2s – d = 2
__________
Adding s = 3 

QUESTION: 13

The total of the ages of Ram, Shyam & Mohan is 96 years. What was the total of their ages three years ago?

Solution:

Total ages of 3 persons = 96.
Three years ago, total age of 3 persons
= 96 – 3 – 3 – 3
= 96 – 9 = 87 years 

QUESTION: 14

Mr. Sharma is three times as old as his son. Five years back, he was four times as old as his son. What is the age of Mr. Sharma?

Solution:

Let son’s age be x.
Mr. Sharma’s age = 3x.
A/Q, 3x – 5 = 4 (x – 5)
⇒ 3x – 5 = 4x – 20 
⇒ 4x – 3x = – 5 + 20 
⇒ x = 15
Age of Mr. Sharma = 3x = 3 × 15 = 45 years. 

QUESTION: 15

A train is running at the speed of 72 km/hr In how many seconds it will cross an electric pole if the length of the train is 360m?

Solution:

Speed of train = 72 km/hr.

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