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Q:

The ratios of areas of two squares, one having its diagonal double than the other is

A) 2:1	B) 2:3
C) 3:1	D) 4:1

Answer & Explanation Answer: D) 4:1

Explanation:

ratio = $\frac{(1 / 2) \times {(2 d)}^{2}}{\frac{1}{2} d^{2}} = 4 : 1$

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Q:

The ratio of the area of a square to that of the square drawn on its diagonal is

A) 1:2	B) 2;3
C) 3:1	D) 4:1

Answer & Explanation Answer: A) 1:2

Explanation:

ratio = $\frac{a^{2}}{{(\sqrt{2 a})}^{2}}$

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Q:

The area of a square field is 69696sq.cm..its diagonal will be equal to

A) 373	B) 573
C) 473	D) 673

Answer & Explanation Answer: A) 373

Explanation:

$d = \sqrt{2 * s} = > d = \sqrt{2 * 69696}$

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Q:

If the length of the diagonal of a square is 20cm,then its perimeter must be

a. $40 \sqrt{2}$ cm b. $30 \sqrt{2}$ cm c. 10cm d. 15 $\sqrt{2}$ cm

A) a	B) b
C) c	D) d

Answer & Explanation Answer: A) a

Explanation:

We know that d=√2s

Given diagonal = 20 cm

=> s = 20/ $\sqrt{2}$ cm

Therefore, perimeter of the square is 4s = 4 x 20/ $\sqrt{2}$ = 40 $\sqrt{2}$ cm.

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Q:

Amy has to visit towns B and C in any order. The roads connecting these towns with her home are shown on the diagram. How many different routes can she take starting from A and returning to A, going through both B and C (but not more than once through each) and not travelling any road twice on the same trip?

A) 10	B) 8
C) 6	D) 4

Answer & Explanation Answer: B) 8

Explanation:

Amy can travel clockwise or anticlockwise on the diagram.

Clockwise, she has no choice of route from A to B, a choice of one out of two routes from B to C, and a choice of one out of two routes from C back to A. This gives four possible routes.

Similarly, anticlockwise she has four different routes.

Total routes = 8

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Filed Under: Time and Distance
Exam Prep: GRE

Q:

A man walking at the speed of 4 kmph crosses a square field diagonally in 3 meters.The area of the field is

A) 10000	B) 20000
C) 30000	D) 40000

Answer & Explanation Answer: B) 20000

Explanation:

speed of the man = 4 x (5/18) m/sec = 10/9 m/sec

time taken = 3 x 60 sec = 180 sec

length of diagonal = speed x time = (10/9) x 180 = 200m

Area of the field = (1/2) x (dioagonal)²

= (1/2) x 200 x 200 sq.m = 20000sq.m

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Q:

A man walked diagonally across a square plot. Approximately what was the percent saved by not walking along the edges?

A) 10%	B) 20%
C) 30%	D) 40%

Answer & Explanation Answer: C) 30%

Explanation:

let the side of the square be x meters
length of two sides = 2x meters
diagonal = $\sqrt{2 x}$ = 1.414x m

saving on 2x meters = .59x m

saving % = $\frac{0.59 x}{2 x} * 100$ %

= 30% (approx)

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Q:

A took 15 seconds to cross a rectangular field diagonally walking at the rate of 52 m/min and B took the same time to cross the same field along its sides walking at the rate of 68m/min. The area of the field is?

A) 50	B) 60
C) 70	D) 80

Answer & Explanation Answer: B) 60

Explanation:

length of the diagonal = 52 x (15/60) =13m

sum of length and breadth = 68 x (15/60) = 17m

$(\sqrt{l^{2} + b^{2}}) = 13 o r l + b = 17$

area =lb = 1/2[(2lb)] = 1/2[(l+b)² - (l²+b²)] = 1/2[17² -169]

=1/2 x 120 = 60 sq.m

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