In GRE Quantitative section , you are likely to encounter at least one problem each on Work and Time, Numbers, Mixtures, Probability, Clock and Calendars.
Here are some sample problems to familiarize you.
Try to solve them by yourself before looking at the solution.
I Arithmetic
Find the number of integers between 100 and 1000 that are divisible by 6.
A. 149 B. 160 C. 150 D. 184 E.166
Solution:
The numbers between 100 and 1000 that are multiples of 6 are 102,108,114,......996
This forms an A.P series with First term: a=102, Common Difference:d=6, last term=996.
Using formula for A.P series:
a+(n-1)d = nth term
102 + (n-1)6 = 996
n=150
Hence answer is C.
Given 0<x<1, which of the following lists the numbers in increasing order?
A. x,x^2,x^(1/2) B. x^1/2,x,x^2 C. x^2,x^(1/2),x D. x,x^(1/2),x^2
E. x^2,x,x^(1/2)
Solution:
For a number between between 0 and 1 , square of a number is less than the number itself and square root of a number is greater than the number.
Hence answer is E as x > x^2 and x < x^(1/2).
II Work and Time
Suzanne and Melody can paint home in 10 and 15 days respectively. They started painting but unfortunately Suzanne has to leave after some days and Melody finished remaining task in 5 days. After how many days did Suzanne left?
A. 10 B. 4 C. 5 D. 20 E. 6
Solution:Melody can complete task in 15 days.
So, Melody 1 day's work = 1/15
Since Melody works for 5 days alone.
So she does 5/15 i.e 1/3rd of work after Suzanne Left.
Hence both of them completed together (1- 1/3) = 2/3rd of the work.
Let both of them work together for x days which is
equivalent to number of days after which Suzanne Left.
Suzanne 1 day's work = 1/10
x[(1/10)+(1/15)]=2/3
x*(5/30)=2/3
x=4
Hence answer is B.
III Clocks
What is the angle between the minute and hour hand of a clock when the time is 14:40?
A. 149 B. 160 C. 150 D. 180 E.130
Solution:
The minute hand moves 360o in an hour. In 40 minutes , it moves by (40/60)*360= 240o.
The hour hand moves by 30 degrees in an hour.
So angle between hour and minute hand (at 14:40)will be somewhere around 240-60=180.
However an hour hand will be ahead of 2 at 14:40. In 40 minutes it will move by (30/60)*40 = 20 degrees.
Hence the angle between hour and minute hand will be 180 - 20 = 160o .
IV Mixtures
How many litres of a solution A that is 15% alcohol must be added to 25 litre solution B that is 5% alcohol so that resulting solution is 10% alcohol.
A. 15 B. 25 C. 20 D. 10 E. 30
Solution:
Solution A: Let x be the litres of 15% solution. Concentration of alcohol: 15% * x.
Solution B: Concentration of alcohol in 25 litres sol : 5% * 25
Resulting Solution : (x+25) litres. Concentration of alcohol: 10%(x+25)
Concentration of alcohol in x litres sol A+ Concentration of alcohol in 25 litres sol B= Concentration of alcohol in resulting sol
(15% * x) + (5% 25 )= [10% * (x+25)]
Solving we get x= 25.
Hence answer is B.
Point to Remember: The combined total of concentration in two parts must be same as the whole solution.
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