Ratio and Two Variable Problems

1. Session for GRE
Ratios and Two variable problems
1

2. Session for GRE
Topics
• Introduction to Linear Equations
• Age related Problems
• Digits related problems
• Ratios
• Proportion
• Variation
2

3. Session for GRE
Introduction to Linear Equations
What is a polynomial?
Degree of a polynomial
2x3 + 9xy + 28
4x3 + 9x2y + 5z2
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4. Session for GRE
• Problem types
• Age related problems
4

5. Session for GRE
Problem Types – Age related problems
Four years ago, the age of a person was four times the age of his son. Four
years hence the age of the person will be 8 years less than 3 times the age of
his son. How may years from now will the sum of their ages be 90?
A) 21 B) 12 C) 24 D) 18 E) 20
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6. Session for GRE
X says to Y, “ I am twice as old as you were when I was as old as you are”.
The sum of their present ages is 63 years. Find the present age of X.
A) 24 B) 39 C) 36 D) 42 E) 48
Problem Types – Age related problems 6

7. Session for GRE
Factors of a Number - Problems
In 12 years, Pollock’s age (which is currently p) will be thrice Amit’s age (which is currently a).
A. Quantity A is greater.
B. Quantity B is greater.
C. The two quantities are equal.
D. The relationship cannot be determined from the information given.
Quantity A
p-24
Quantity B
3q
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8. Session for GRE
• Problem types
• Digits related problems
8

9. Session for GRE
Digits related problem - Concept
Concept: Number formed by reversing the digits
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10. Session for GRE
A) 51 B) 62 C) 72 D) 84 E) 48
Problem Types – Digits related problem
A two digit number is such that the sum of its digits is thrice the difference of its digits. If the number
exceeds the number formed by reversing its digits by 36. Find the number.
10

11. Session for GRE
•Ratios
11

12. Session for GRE
What are ratios? 12

13. Session for GRE
Problems - Ratios
Two numbers are in the ratio 3 : 5. If each number is increased by 10, the ratio becomes 5 : 7.
Find the sum of the numbers.
A. 24
B. 40
C. 72
D. 16
E. 48
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14. Session for GRE
Combining ratios 14

15. Session for GRE
Problems - Ratios
In one day, Anmol receives 4 messages for every 3 messages of Tom and Tom receives 3
messages for every 2 messages of Kiran. How many messages does Tom receive if if Anmol
receives 10 messages more than Kiran?
A. 20
B. 15
C. 12
D. 16
E. 18
15

16. Session for GRE
•Proportion
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17. Session for GRE
What is a proportion? 17

18. Session for GRE
Problems - Ratios
If A is proportional to B and A = 3 and B = 2, find the value of A when B = 10
A. 20
B. 15
C. 12
D. 16
E. 18
18

19. Session for GRE
•Variation
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20. Session for GRE
What is a variation? 20

21. Session for GRE
Variations - Problems
If 8 men can paint 28 rooms in a day, then how many men can paint 70 rooms in 2 days?
A. 10
B. 20
C. 40
D. 15
E. 25
21

22. Session for GRE
Variations - Problems
A family of 10 persons have ration for 30 days. After 10 days 2 persons go out. How long will the remaining
ration last?
A. 10
B. 20
C. 18
D. 15
E. 25
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