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Q:

Which fraction comes next in the sequence

$\frac{2}{3}, \frac{1}{3}, \frac{5}{27}, \frac{7}{81}, ?$

A) 1/27	B) 11/278
C) 9/48	D) 7/123

Answer & Explanation Answer: A) 1/27

Explanation:

Clearly, the numerators of the fractions in the given sequence follow the series of 2, 3, 5, 7,... and the denominator follows 3, 9, 27, 81, 243, ...
Then, the next term in the given sequence is $\frac{9}{3^{5}} = \frac{9}{243} = \frac{1}{27}$ .

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Q:

Choose what replaces '?' in the following figure ?

creative111486456294.jpg image

A) Q	B) O
C) M	D) N

Answer & Explanation Answer: D) N

Explanation:

The alphabetical value of the letters in the left hand column follows through the sequence of Prime Numbers, with the letters in the right hand column representing the corresponding reverse alphabetical values. So,

M = Reverse of M = N.

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Q:

40% of 265 + 35% of 180 = 50% of ?

A) 383	B) 338
C) 84.5	D) 253.5

Answer & Explanation Answer: B) 338

Explanation:

We know that 40% = $\frac{2}{5}$

40% of 265 + 35% of 180 = 50% ?

$\frac{2}{5}$ x 265 + 35% of 180 = 50% ?

We know that (35% of 180 = 180% of 35) & 180% = $\frac{9}{5}$

$\frac{2}{5}$ x 265 + $\frac{9}{5}$ x 35 = 50% ?

106 + 63 = 50% ?

?= 2 x 169 = 338.

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Q:

If (2a + 3b)/(5a - 3b) = 23/5 , then the value of ba is ?

A) 5	B) 4
C) 20	D) 28

Answer & Explanation Answer: C) 20

Explanation:

Given (2a + 3b)/(5a - 3b) = 23/5
=> 10a + 15b = 115a - 69b
=> 105a = 84b => 5a = 4b
a/b = 4/5 => a=4 & b=5
=> bxa = 5x4 = 20.

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Filed Under: Ratios and Proportions
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Q:

If y/(x - z) = (y + x)/z = x/y then find z : y : x ?

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

Answer & Explanation Answer: B) 3:2:4

Explanation:

Given, y/(x - z) = (y + x)/z = x/y
$y z = x y + x^{2} - y z - x z . . . . (1)$
Also $\frac{x}{y} = \frac{y}{x - z}$ $\Rightarrow x^{2} - x z = y^{2} . . . . (2)$
Using (1) and (2), we get yz = xy - yz + $y^{2}$
2yz = xy + $y^{2}$
2z = x + y
Only option (B) satisfies the equation.

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Q:

If $\log_{7} (2)$ = m, then $\log_{49} (28)$ is equal to ?

A) 1/(1+2m)	B) (1+2m)/2
C) 2m/(2m+1)	D) (2m+1)/2m

Answer & Explanation Answer: B) (1+2m)/2

Explanation:

$\log_{49} (28) = \frac{1}{2 \log_{7} (7 \times 4)}$

= $\frac{1}{2} + \frac{1}{2} (2 \log_{7} (2))$
= $\frac{1}{2} + \log_{7} (2)$
= $\frac{1}{2} + m$
= $\frac{1 + 2 m}{2}$ .

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Filed Under: Logarithms
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Q:

If $a^{2} + b^{2} = c^{2}$ , then $\frac{1}{l o g_{c + a} (b)} + \frac{1}{l o g_{c - a} (b)} = ?$

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

Answer & Explanation Answer: B) 2

Explanation:

Given $a^{2} + b^{2} = c^{2}$

Now $\frac{1}{\log_{c + a} (b)} + \frac{1}{\log_{c - a} (b)}$

= $\log_{b} (c + a) + \log_{b} (c - a)$

= $\log_{b} (c^{2} - a^{2})$

= $2 \log_{b} (b) = 2$

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Q:

A man walks 6 km at a speed of $1 \frac{1}{2}$ kmph, runs 8 km at a speed of 2 kmph and goes by bus another 32 km. Speed of the bus is 8 kmph. Find the average speed of the man in kmph.

$A) 4 \frac{3}{14}$

B) $4 \frac{2}{13}$

C) $2 \frac{4}{13}$

D) $3 \frac{4}{14}$

A) Option A	B) Option B
C) Option C	D) Option D

Answer & Explanation Answer: B) Option B

Explanation:

Man walked 6 km at 1.5 kmph, again he walked 8 km at speed of 2 kmph and 40 km at a speed of 8kmph
time taken indivisually:
=> 6/1.5 = 4 m
=> 8/2 = 4 m
=> 40/8 = 5 m

Average speed of man= total distance/ total time
=> 54/13 = $4 \frac{2}{13}$ kmph

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Filed Under: Time and Distance
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