Gmat Prep_02

gdk800 wrote:1) If n denotes a number to the left of 0 on the number line such that square of n is less than 1/100. Then reciprocal of n must be
a. Less than -10.
b. Between -1 and -1/10.
c. Between -1/10 and 0.
d. Between 0 and 1/10.
e. Greater than 10.

OA is A

gdk800 wrote:2) A car averages 25 miles/gallon when driven in city and 40 miles/gallon when driven on highway. According to these rates, which of following is closest to the number of miles per gallon that the car averages when it is driven 10 miles in the city and then 50 miles on the highway?
a. 28
b. 30
c. 33
d. 36
e. 38

OA is D

gdk800 wrote:3) Attached is an image. On the number line, its visible that according to Option B (z>y) is true but its not the OA.

OA is E

• (1) x + y > y => As x and y both negative (x + y) certainly less than both x and y. INCORRECT
  (2) xz > xy => Explained earlier! (Another explanation : x and y negative but z positive => xz always negative and xy always positive => xy > xz) INCORRECT
  (3) tz < z => As z is positive this implies t < 1. INCORRECT
  (4) m^u < 0 => m = -1, u = 2 => m^u = 1. INCORRECT
  (5) t^m > 0 => t is positive and m = -1 => t^m = t^(-1) = 1/t > 0. CORRECT

gdk800 wrote:Thanks Rahul, yes i realized about the 3rd question as soon as you wrote x is less than 0.
But could you please elaborate on the 1st question a bit more.

As n > -1/10
=>10 > -1/n [As n is negative, cross multiplication will also revert the inequality sign! Thus it will be 10 < -1/n]
Multiplying both sides by -1 and thus the inequality reverses sign
=>-10 < 1/n

Thus 1/n should be greater and not less than -10.....

Plz explain!!!