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Q:

There are 209 doctors and nurses in a hospital. If the ratio of the doctors to the nurses is 11 : 8, then how many nurses are there in the hospital?

A) 88	B) 96
C) 108	D) 121

Answer & Explanation Answer: A) 88

Explanation:

Given,
The ratio of the doctors to the nurses is 11 : 8
Number of nurses = 8/19 x 209 = 88.

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Q:

Who among the following took over as the 25th Director General of the Border Roads(DGBR) ?

A) Lt. Gen. Suresh Sharma	B) Lt. Gen. David R. Syiemlieh
C) Lt. Gen. Srikanth Mishra	D) Lt. Gen. Sanjeev Kumar Shrivastava

Answer & Explanation Answer: D) Lt. Gen. Sanjeev Kumar Shrivastava

Explanation:

Lt. Gen. Sanjeev Kumar Shrivastava took over as the 25th Director General of the Border Roads (DGBR). He has replaced Lt. Gen. Suresh Sharma. Prior to it, he was holding the appointment of Director General Combat Engineers at Integrated Headquarters of Ministry of Defence(Army).

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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:

Which one of the following foreign agencies will assist the municipal agencies to improve quality of municipal schools through its School Excellence Programmes(SEP) ?

A) IMF	B) UNDP
C) ADB	D) UNICEF

Answer & Explanation Answer: C) ADB

Explanation:

Asian Development Bank (ADB) announced that it will assist the municipal agencies to improve quality of municipal schools through its School Excellence Programme (SEP).

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Q:

If x is a whole number, then x²(x² - 1) is always divisible by ?

A) 4	B) 8
C) 12	D) None

Answer & Explanation Answer: C) 12

Explanation:

we can do this by trial and error method.

Putting x = 2,we get 2²(2² - 1) = 12.
checking with other integers, the above equation always gives a value which is a multiple of 12,
So, x²(x² - 1) is always divisible by 12.

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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 x and y are the two digits of the number 653xy such that this number is divisible by 80, then x+y is equal to ?

A) 5	B) 4
C) 3	D) 2

Answer & Explanation Answer: D) 2

Explanation:

Since 653xy is divisible by 5 as well as 2, so y = 0.
Now, 653x0 must be divisible by 8.
So, 3x0 must be divisible by 8. This happens when x = 2
x + y = (2 + 0) = 2.

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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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