My answers as below :

1. (1/5)^m * (1/4)^18 = 1/(2(10)^35), the correct answer is 35.

On the left hand side (LHS), we have (1/5)^m multiplied by (1/4)^18 which can also be written as (1/2)^36, also as 1/2 * (1/2)^35.

Hence LHS is (1/5)^m * 1/2 * (1/2)35

On the right hand side (RHS), we have 1/2 * (1/10)35 = 1/2 * (1/5)35 * (1/2)35

Equating LHS and RHS, 1/2 * (1/2)35 cancels out and leaves us with (1/5)^m = (1/5)^35.

Hence m = 352. Based on the information given, the correct answer should be 81 and not 27.

It should be a typo.3. 1st statement: The range of A is less than the range of B. i.e the difference between the greatest and least heights is more for B than for A.

2nd statement: The greatest height of A is more than the greatest height of B.

Now putting the two statements together, the least height of A should be more than the least height of B, as the range for A is less than the range for B.

I would mark it to be C.4. 1st statement : X - Y = 1/2 (E.g X = 3/4, Y = 1/4 OR X = 1/4, Y = -1/4 OR X = -1/4, Y = -3/4)

2nd statement : X > Y ( E.g X = -2, Y = -4 OR X = 4, Y = 2 OR X = 4, Y = -2 OR X = 1/4, Y = -1/4 OR X = 3/4, Y = 1/4 OR X = -1/4, Y = -3/4)

Both the statements are ambiguous. Putting them together, also doesn't tell if X and Y are both positive.

I would mark it to be E.5. 1st statement helps us in getting the ratio of women to men ( W/C = 5/2, C/M = 5/11. Multiply W/C by 5/5 = 25/10. Multiply C/M by 2/2 will make it 10/22, hence W/M = 25/22)

2nd statement just tells that W is less than 30, it can be anything. Doesn't help in identifying the total # of people.

I would mark it to be E again.
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