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GRE QUANT:
ARITHMETIC
Question 1
How many ounces of a solution that is 30% salt must be added to a 50 ounce solution that
is 10% salt so that the resulting solution is 20 % salt.
a) 20. b) 30. c) 40. d) 50. e) 60
Let x ounces of the solution be added to the 50 ounce solution
Resulting solution = 50 +x
Resulting solution is 20 % salt
ie
20
100
× 50 + 𝑥
The solution which is added is 30% salt
ie
30
100
× 𝑥
The 50 ounce solution is 10 % salt
ie
10
100
× 50
20
100
× 50 + 𝑥 =
30
100
𝑥+
10
100
× 50
20 50 + 𝑥 = 30 𝑥 + 500
1000 + 20 x = 30 x +500
10 x = 500
x = 50
Question 2
A has 20 coins consisting of quarters and dimes. If A has a total of $3.05, how
many dimes does A have
Let A have x dimes
Then A has 20 – x quarters
10 x + (20 – x )25 = 305
10x + 500 – 25 x = 305
195 = 15 x
x = 13
A has 13 dimes
Question 3
A is 20 years older than B. In 10 years, B’s age will be half that of A’s
What is B’s age
A B
x+20 x
10 years later
x+30
x+10
𝑥 + 10 =
1
2
(𝑥 + 30) 2x +20 = x +30
x = 10
B’s age = 10
Question 4
Working together at a constant rate, machines L,M and N can produce a total of
200 bolts in 4 hours. If machine L can produce 20 bolts in 30 minutes and machines
M and N work at the same constant rate as each other, how many bolts can
Machine M produce in 1 hour
Machines L, M and N produce 200 bolts in 4 hours
They produce
200
4
= 50 𝑏𝑜𝑙𝑡𝑠 in 1 hour
L produce 20 bolts in 30 minutes
L produces 40 bolts in 1 hour
Let M and N produce x bolts in 1 hour
40 +2x = 50
2𝑥 = 10
x = 5
Machine M produces 5 bolts in 1 hour
Question 5
O
If the area of the circle with centre O is 36 𝜋
Find the area of the shaded portion. The given triangle
is right angled at O
𝜋𝑟2
= 36𝜋
r = 6
A( shaded portion)= A(quadrant) – A(isosceles right angled triangle)
𝑎𝑟𝑒𝑎 =
1
4
36 𝜋 −
1
2
6(6)
= 9 𝜋 − 18
Question 6
What is 0. 5 % of 55
0.5
100
× 55 = 0.275
Answer = 27. 5 %

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GRE QUANT: ARITHMETIC

  • 2. Question 1 How many ounces of a solution that is 30% salt must be added to a 50 ounce solution that is 10% salt so that the resulting solution is 20 % salt. a) 20. b) 30. c) 40. d) 50. e) 60 Let x ounces of the solution be added to the 50 ounce solution Resulting solution = 50 +x Resulting solution is 20 % salt ie 20 100 × 50 + 𝑥 The solution which is added is 30% salt ie 30 100 × 𝑥 The 50 ounce solution is 10 % salt ie 10 100 × 50
  • 3. 20 100 × 50 + 𝑥 = 30 100 𝑥+ 10 100 × 50 20 50 + 𝑥 = 30 𝑥 + 500 1000 + 20 x = 30 x +500 10 x = 500 x = 50
  • 4. Question 2 A has 20 coins consisting of quarters and dimes. If A has a total of $3.05, how many dimes does A have Let A have x dimes Then A has 20 – x quarters 10 x + (20 – x )25 = 305 10x + 500 – 25 x = 305 195 = 15 x x = 13 A has 13 dimes
  • 5. Question 3 A is 20 years older than B. In 10 years, B’s age will be half that of A’s What is B’s age A B x+20 x 10 years later x+30 x+10 𝑥 + 10 = 1 2 (𝑥 + 30) 2x +20 = x +30 x = 10 B’s age = 10
  • 6. Question 4 Working together at a constant rate, machines L,M and N can produce a total of 200 bolts in 4 hours. If machine L can produce 20 bolts in 30 minutes and machines M and N work at the same constant rate as each other, how many bolts can Machine M produce in 1 hour Machines L, M and N produce 200 bolts in 4 hours They produce 200 4 = 50 𝑏𝑜𝑙𝑡𝑠 in 1 hour L produce 20 bolts in 30 minutes L produces 40 bolts in 1 hour
  • 7. Let M and N produce x bolts in 1 hour 40 +2x = 50 2𝑥 = 10 x = 5 Machine M produces 5 bolts in 1 hour
  • 8. Question 5 O If the area of the circle with centre O is 36 𝜋 Find the area of the shaded portion. The given triangle is right angled at O 𝜋𝑟2 = 36𝜋 r = 6 A( shaded portion)= A(quadrant) – A(isosceles right angled triangle)
  • 9. 𝑎𝑟𝑒𝑎 = 1 4 36 𝜋 − 1 2 6(6) = 9 𝜋 − 18
  • 10. Question 6 What is 0. 5 % of 55 0.5 100 × 55 = 0.275 Answer = 27. 5 %