GATE Questions

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Let 1 woman's 1 day work = x.

Then, 1 man's 1 day work = x/2 and 1 child's 1 day work  x/4.

So, (3x/2 + 4x + + 6x/4) = 1/7

28x/4 = 1/7 => x = 1/49

1 woman alone can complete the work in 49 days.

So, to complete the work in 7 days, number of women required = 49/7 = 7.

1 x 1 + 1 x 1 = (1 + 1) = 2

2 x 2 + 2 x 2 = (4 + 4) = 8

8 x 3 + 3 x 3 = (24 + 9) = 33

33 x 4 + 4 x 4 = (132 + 16) = 148

148 x 5 + 5 x 5 = (740 + 25) = 765.

The sum of square of two no is 116 i.e no lie 1-11, because 11x11 =121 which is greater than 116
again after cheaking all possible pair of no only 4 and 10 satisfy this condsn , again the progression is of positive integer so 10 cant not be 1st term
so the 1st term is 4,
but from the 2nd we cant able to find the 1st term

so only 1st statement is sufficient to answer the question

The given number series is 3, 5, 13, 43, 167

3

3 x 1 + 2 = 5

5 x 2 + 3 = 13

13 x 3 + 4 = 43

43 x 4 + 5 = 177 (not equal to 167)

Hence, the odd number in the given number sequence is 167. 

Here the series of the form is x2 - 1, x2 - 2, x2 - 3,...

 53 x 2 - 4 = 106 - 4 = 102

The given series 16, 254, 1296, 4096, 10000 follows a pattern that

24, 44, 64, 84, 104,...

Hence, the odd man in the series is 4 x 4 x 4 x 4 = 256 not 254.

504/42 × 7 - 63 + 28 = 84 – 63 + 28 = 49

Hence option 5 is correct.

Lets say shyam sells at 100,

Since Ram sells 25% cheaper than Shyam,

Therefor Ram sells at less than 25% of100 or 75 rs.

Ram sells 25% dearer than Bram or 125% of Ram =100% of Bram or

125% of x (say x price of bram )=75rs.
or 100% of x =60rs.
hence price of bram is 60rs.

now Bram's good is cheaper than Shyam's as (100-60)x100/100% or 40%.

Hence Brams Good is 40% cheaper than that of Shyam's good.