7th GRADE MATH PROBLEMS WITH ANSWERS

Question 1 :

A clock is sold for $189 at a loss of 10%.What is the cost price of clock ? 

(A) $210             (B) $251          (C) $182

Solution :

Selling price of clock  =  $189

Loss  =  10%

Let x be the cost price 

Cost price  =  [100 / (100 - Loss%)] ⋅ Selling price

=  [100 / (100 - 10)] ⋅ Selling price

=  (100 / 90) ⋅ 189

=  $210

So, the required cost price is $210.

Question 2 :

Find the discount on a book marked at $180 and discount at 15%.

(A) 18            (B) 13              (C) 27

Solution :

Marked price  =  $180

Discount  =  15%

  =  15% of 180  

  =  (15/100) ⋅ 180

  =  27

So, the discount on the book is $27.

Question 3 :

The three angles of quadrilateral are 78°, 105°, 120° 

(A) 95°               (B) 57°              (C) 90°

Solution :

The sum of angles in a quadrilateral  =  360°

Let x be the unknown angle

78 + 105 + 120 + x  =  360

303 + x  =  360

x  =  360 - 303

x  =  57

So, the fourth angle is 57°

Question 4 :

Squares of even numbers are always ____________

(A) odd                (B) even         (C) neither odd nor even

Solution :

Squares of even numbers are always even

Question 5 :

625 students are sitting in a lawn in such a way that there is many students in a row as there are rows in a lawn. Find the number of rows in a lawn.

(A) 25         (B) 15           (C) 35

Solution :

Number of students in one row  =  Number of rows in the lawn

From this information, we come to know that the number of students has to be decomposed as the product of the same numbers.

For this let us find the square root of 625

√625  =  √25 ⋅ 25

  = 25

Hence the number of rows in a lawn is 25.

Question 6 :

Which of the following are cubes of even numbers?

(A) 216       (B) 1331         (C) 3375

Solution :

The product of two or more even numbers is always even.

Here 216 is even number, so it can the cube of even number.

216  =  6 ⋅ 6 ⋅ 6

  =  6³

Hence 216 is the cube of 6. 

Question 7 :

The volume of a cubical box is 46.656 cubic meters. Find the length of the side of a cubical box ?

(A) 1.5 m       (B) 2.6 m        (C) 3.6 m

Solution :

Volume of cubical box  =  46.656 cubic meters

a³  =  46.656

a  =  3.6 m 

Hence the side length of cubical box is 3.6 m

Question 8 :

Simplify √84 ÷ √7 

(A) 2√5       (B) 2√3       (C) 3√2

Solution :

√84 ÷ √7   =  √(84/7)

  =   √12

=   √(2⋅2⋅3)

=  2 √3

Question 9 :

By selling the watch for $785 a dealer losses 5%. Find the cost price.

(A) $715.12      (B) $815.20      (C) $826.32

Solution :

Let "x" be the cost price

Cost price  =  [100 / (100 - loss %)] Selling price

  =  [100 / (100 - 5)] 785

  =  (100 / 95)785

  =  826.3

Hence the cost price of the watch is $826.

Question 10 :

If the same number is added to both the numerator and denominator of a fraction 3/5, then the result is 3/4.Find the number. 

(A) 2          (B) 5         (C) 3

Solution :

Let x be the required number to be added to both numerator and denominator 

(3 + x) / (5 + x)  =  =  3 / 4

4(3 + x)  =  3(5 + x)

12 + 4x  =  15 + 3x

4x - 3x  =  15 - 12

x  =  3

So, 3 is the required number to be added to both numerator and denominator.

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