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Question (21)

QN0036641

The product of two consecutive positive integers is 306. The smaller integer is:

(A) 16
(B) 17
(C) 18
(D) 19

Correct Answer: B

Explanation:

Let the smaller integer be x. Then x(x+1)=306, so x²+x−306=0=(x−17)(x+18). Thus x=17.

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Question (22)

QN0036642

Two numbers have sum 27 and product 182. The numbers are:

(A) 12 and 15
(B) 13 and 14
(C) 10 and 17
(D) 7 and 20

Correct Answer: B

Explanation:

The numbers are roots of x²−27x+182=0=(x−13)(x−14).

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Question (23)

QN0036643

The area of a rectangle is 528 m². Its length is one metre more than twice its breadth. If the breadth is x m, which equation represents the situation?

(A) 2x²+x−528=0
(B) 2x²−x−528=0
(C) x²+2x−528=0
(D) 2x²+x+528=0

Correct Answer: A

Explanation:

Length=2x+1. Therefore x(2x+1)=528, giving 2x²+x−528=0.

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Question (24)

QN0036644

The product of two consecutive positive integers is 156. The larger integer is:

(A) 11
(B) 12
(C) 13
(D) 14

Correct Answer: C

Explanation:

x(x+1)=156 gives x²+x−156=0=(x−12)(x+13). Thus the integers are 12 and 13.

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Question (25)

QN0036645

A rectangle has area 800 m², and its length is twice its breadth. Its breadth is:

(A) 10 m
(B) 15 m
(C) 20 m
(D) 25 m

Correct Answer: C

Explanation:

Let breadth=x. Then length=2x. Hence 2x²=800, so x=20 m.

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Question (26)

QN0036646

A rectangle has perimeter 80 m and area 400 m². Its dimensions are:

(A) 10 m and 30 m
(B) 15 m and 25 m
(C) 20 m and 20 m
(D) 5 m and 35 m

Correct Answer: C

Explanation:

l+b=40 and lb=400. Therefore l=b=20 m.

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Question (27)

QN0036647

A mother is 26 years older than her son. Three years from now, the product of their ages will be 360. If the son's present age is x, which equation is obtained?

(A) x²+32x−273=0
(B) x²+32x−360=0
(C) x²+26x−360=0
(D) x²+29x−360=0

Correct Answer: A

Explanation:

Present ages are x and x+26. Three years later they are x+3 and x+29. Thus (x+3)(x+29)=360, giving x²+32x−273=0.

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Question (28)

QN0036648

A train covers 480 km at speed x km/h. If its speed were 8 km/h less, it would take 3 hours more. Which equation represents the situation?

(A) x²+8x−1280=0
(B) x²−8x−1280=0
(C) x²+8x+1280=0
(D) x²−8x+1280=0

Correct Answer: B

Explanation:

480/(x−8)=480/x+3. Simplifying gives x²−8x−1280=0.

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Question (29)

QN0036649

A right triangle has hypotenuse 13 cm and one leg is 7 cm less than the other. The shorter leg is:

(A) 5 cm
(B) 6 cm
(C) 7 cm
(D) 8 cm

Correct Answer: A

Explanation:

Let shorter side=x and longer side=x+7. Then x²+(x+7)²=169. The positive solution is x=5 cm.

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Question (30)

QN0036650

A number is such that its square exceeds five times the number by 24. Which equation represents it?

(A) x²+5x+24=0
(B) x²−5x−24=0
(C) x²+5x−24=0
(D) x²−5x+24=0

Correct Answer: B

Explanation:

x²=5x+24, so x²−5x−24=0.

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Question (21)

The product of two consecutive positive integers is 306. The smaller integer is:

Explanation:

Link:

Question (22)

Two numbers have sum 27 and product 182. The numbers are:

Explanation:

Link:

Question (23)

The area of a rectangle is 528 m². Its length is one metre more than twice its breadth. If the breadth is x m, which equation represents the situation?

Explanation:

Link:

Question (24)

The product of two consecutive positive integers is 156. The larger integer is:

Explanation:

Link:

Question (25)

A rectangle has area 800 m², and its length is twice its breadth. Its breadth is:

Explanation:

Link:

Question (26)

A rectangle has perimeter 80 m and area 400 m². Its dimensions are:

Explanation:

Link:

Question (27)

A mother is 26 years older than her son. Three years from now, the product of their ages will be 360. If the son's present age is x, which equation is obtained?

Explanation:

Link:

Question (28)

A train covers 480 km at speed x km/h. If its speed were 8 km/h less, it would take 3 hours more. Which equation represents the situation?

Explanation:

Link:

Question (29)

A right triangle has hypotenuse 13 cm and one leg is 7 cm less than the other. The shorter leg is:

Explanation:

Link:

Question (30)

A number is such that its square exceeds five times the number by 24. Which equation represents it?

Explanation:

Link:

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