solutions for updated pattern of tcs

1. If a/b > 1, which of the following must be less than 1?

a) sqrt(a/b)

b) a/b^2

c)a/2b

d) b/a

ans:From the question stem, we know that a must be greater than b. A leaves us with a square root of something greater than 1; this value must also be greater than 1. B could be less than 1; if a=2 and b=3, for instance. However, if a=8 and b=2, then a / b2 is greater than 1. Similarly, C could be less than 1 but doesn’t have to be. . d moves the bigger value to the denominator, creating a fraction less than 1.

2. For the positive integers x, x + 2, x + 4, x + 7, and x + 12, the mean is how much greater than the median?

a) 0

b) 1

c) 2

d) 3 

ans : The median of the set is the middle value, x + 4.

The mean is (x+x+2+x+4+x+7+x+12)5, which simplifies to (5x+25)5, or x + 5.

(x + 5) - (x + 4) gives us a difference of 1 between the mean and median.

3. What is the smallest integer a for which 27^a > 3^24?

a) 7

b) 8

c)9

d) 10

ans:n order to solve, we must find a common base. Since 27 = 33, we can rewrite the inequality as (33)a > 324, or 33a > 324. Since we now have a common base, we can rewrite the inequality using only the exponents: 3a > 24, or a > 8. Be careful not to answer 8; that would make the two sides equal.

4. a is the hundreds digit of the three digit integer x, b is the tens digit of x, and c is the units digit of x. a = 2b = 4c, and a > 0. What is the difference between the two greatest possible values of x?

a) 124

b) 297

c)394

d)421

sol:

if a = 2b = 4c and a, b, and c must all be nonzero single digit integers - if they weren't, they couldn't be digits - then c is either 1 or 2. If c = 1, then b = 2 and a = 4, giving us 421. If c = 2, then b = 4 and a = 8, giving us 842.

The difference between the numbers is thus 842 - 421 = 421 = (D).