GATE Questions

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First girl facing North
Then she rotates 100 deg clock wise => 10 deg ES
Then again she rotates 190 deg anti clock wise => for 100 deg it is North and more 90 deg means West.
Therefore, the new direction of the girl is West.

Let the C.P of one item is Rs. P
and that of other is Rs. (7500 - P)

According to the data given
C.P = S.P
=> Px(116/100) + (7500-P)x(86/100) = 7500
=> 30P = 105000
=> P = 3500

Required difference between selling prices
= Rs. [(3500/100) x 116] - [(4000/100) x 86]
= 4060-3440
= Rs. 620

Given R + S + M + D = 76

=> R+7 : S+7 : M+7 : D+7 = 7:6:5:8

=> Let the ratio = x

=> M+7 = 5x

=> M = 5x-7

=> R = 7x-7

=> S = 6x-7

=> D = 8x-7

=> R + S + M + D = 76

=> 7x-7 + 6x-7 + 5x-7 + 8x-7 = 76

=> 26x - 28 = 76

=> 26x = 104

=> x = 4

=> Mahesh's present age = 5x-7 = 20 - 7 = 13 years.

Given there are 9 flavours of ice creams.

Each child takes the combination of two flavours and no two children will have the same combination

This can be done by  ways i.e children.

Number of children=C29  = 9 x 8 / 1x 2 = 36.

From the given data,

12 children 16 days work,
One child’s one day work = 1/192.

8 adults 12 days work,
One adult’s one day’s work = 1/96.

Work done in 3 days = ((1/96) x 16 x 3) = 1/2

Remaining work = 1 – 1/2 = 1/2

(6 adults+ 4 children)’s 1 day’s work = 6/96 + 4/192 = 1/12

1/12 work is done by them in 1 day.

1/2 work is done by them in 12 x (1/2) = 6 days.

The ratio of their investments:
50000x36 : 80000x30 = 3 : 4
Simran's share of profit = (24500x3/7) = Rs.10,500.

Here the given pair of words are related in such a way that they are synonyms.

That is Genuine and Authentic are synonyms and similarly, Mrage and illusion are synonyms.

Hence, Genuine : Authentic : : Mirage : Illusion.

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.