A father's age is three times his son's. Their combined age is 44 years. Find the son's age.
Correct answer: C
Let the son's age be x. Then x + 3x = 44, so x = 11.
Quantitative Aptitude
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For the interior-angle sum in degrees of a hexagon, identify the requested value.
Correct answer: D
(6−2)×180=720.
For the probability numerator, in lowest terms, of rolling an even number on a fair six-sided die, identify the requested value.
Correct answer: C
Three of six outcomes are even, so the probability is 1/2.
Evaluate the two proposed answers. Which are supported? I. the area in square centimetres of a triangle with base 14 cm and altitude 9 cm — the requested value: 63. II. the volume in cubic centimetres of a cube with edge 4 cm — the requested value: 198.
Correct answer: A
I is correct: the area in square centimetres of a triangle with base 14 cm and altitude 9 cm → 63. Area=½×14×9. II is incorrect: the volume in cubic centimetres of a cube with edge 4 cm → 64. Volume=4³.
For the number of two-person teams from five distinct people, identify the requested value.
Correct answer: B
Choose two: 5×4/2=10.
Evaluate the two proposed answers. Which are supported? I. the circumference in centimetres of a circle of radius 7 cm, using π=22/7 — the requested value: 54. II. the tenth term of 3,7,11,... — the requested value: 486.
Correct answer: C
I is incorrect: the circumference in centimetres of a circle of radius 7 cm, using π=22/7 → 44. C=2πr=44. II is incorrect: the tenth term of 3,7,11,... → 39. a10=3+9×4.
For the exterior angle in degrees of a regular octagon, identify the requested value.
Correct answer: A
Each exterior angle is 360/8.
Evaluate the two proposed answers. Which are supported? I. the number of ways to arrange four distinct books in a row — the requested value: 24. II. the sum of the first ten terms of 2,4,6,... — the requested value: 13.
Correct answer: C
I is correct: the number of ways to arrange four distinct books in a row → 24. There are 4!=24 permutations. II is incorrect: the sum of the first ten terms of 2,4,6,... → 110. The sum is 2(1+...+10)=110.
For the total surface area in square centimetres of a cube with edge 3 cm, identify the requested value.
Correct answer: B
Six faces each have area 9.
Evaluate the two proposed answers. Which are supported? I. x+y when x−y=4 and x+y is twice x−y — the requested value: 8. II. the positive root of x²−5x−14=0 — the requested value: 4.
Correct answer: D
I is correct: x+y when x−y=4 and x+y is twice x−y → 8. The sum is 2×4. II is incorrect: the positive root of x²−5x−14=0 → 7. The expression factors as (x−7)(x+2).
For the volume in cubic centimetres of a cylinder with radius 3 cm and height 7 cm, using π=22/7, identify the requested value.
Correct answer: B
Volume=πr²h=(22/7)×9×7.
Evaluate the two proposed answers. Which are supported? I. the sixth term of 2,6,18,... — the requested value: 720. II. the exterior angle in degrees of a regular octagon — the requested value: 154.
Correct answer: D
I is incorrect: the sixth term of 2,6,18,... → 486. The geometric sequence gives 2×3^5. II is incorrect: the exterior angle in degrees of a regular octagon → 45. Each exterior angle is 360/8.
For the number of ways to arrange four distinct books in a row, identify the requested value.
Correct answer: A
There are 4!=24 permutations.
Evaluate the two proposed answers. Which are supported? I. the volume in cubic centimetres of a cube with edge 4 cm — the requested value: 24. II. the sum of the first ten terms of 2,4,6,... — the requested value: 13.
Correct answer: D
I is incorrect: the volume in cubic centimetres of a cube with edge 4 cm → 64. Volume=4³. II is incorrect: the sum of the first ten terms of 2,4,6,... → 110. The sum is 2(1+...+10)=110.
For x+y when x−y=4 and x+y is twice x−y, identify the requested value.
Correct answer: B
The sum is 2×4.
Evaluate the two proposed answers. Which are supported? I. the area in square centimetres of a circle of diameter 14 cm, using π=22/7 — the requested value: 198. II. x satisfying 3x+7=31 — the requested value: 7.
Correct answer: C
I is incorrect: the area in square centimetres of a circle of diameter 14 cm, using π=22/7 → 154. Radius is 7, so area=π×49=154. II is incorrect: x satisfying 3x+7=31 → 8. 3x=24, so x=8.
For the tenth term of 3,7,11,..., identify the requested value.
Correct answer: B
a10=3+9×4.
Evaluate the two proposed answers. Which are supported? I. the number of two-person teams from five distinct people — the requested value: 7. II. the number of ways to arrange four distinct books in a row — the requested value: 1.
Correct answer: D
I is incorrect: the number of two-person teams from five distinct people → 10. Choose two: 5×4/2=10. II is incorrect: the number of ways to arrange four distinct books in a row → 24. There are 4!=24 permutations.
For the hypotenuse in centimetres of a right triangle with legs 5 cm and 12 cm, identify the requested value.
Correct answer: C
Pythagoras gives √(25+144)=13.
Evaluate the two proposed answers. Which are supported? I. x²+y² when x+y=10 and xy=21 — the requested value: 110. II. the interior-angle sum in degrees of a hexagon — the requested value: 44.
Correct answer: B
I is incorrect: x²+y² when x+y=10 and xy=21 → 58. (x+y)²−2xy=100−42. II is incorrect: the interior-angle sum in degrees of a hexagon → 720. (6−2)×180=720.
For the area in square centimetres of a circle of diameter 14 cm, using π=22/7, identify the requested value.
Correct answer: D
Radius is 7, so area=π×49=154.
Evaluate the two proposed answers. Which are supported? I. the smaller root of x²−9x+20=0 — the requested value: 4. II. the tenth term of 3,7,11,... — the requested value: 486.
Correct answer: C
I is correct: the smaller root of x²−9x+20=0 → 4. The roots are 4 and 5. II is incorrect: the tenth term of 3,7,11,... → 39. a10=3+9×4.
For the sum of the first ten terms of 2,4,6,..., identify the requested value.
Correct answer: B
The sum is 2(1+...+10)=110.
Evaluate the two proposed answers. Which are supported? I. the volume in cubic centimetres of a cube with edge 4 cm — the requested value: 64. II. the volume in cubic centimetres of a cylinder with radius 3 cm and height 7 cm, using π=22/7 — the requested value: 10.
Correct answer: A
I is correct: the volume in cubic centimetres of a cube with edge 4 cm → 64. Volume=4³. II is incorrect: the volume in cubic centimetres of a cylinder with radius 3 cm and height 7 cm, using π=22/7 → 198. Volume=πr²h=(22/7)×9×7.
For x²+y² when x+y=10 and xy=21, identify the requested value.
Correct answer: B
(x+y)²−2xy=100−42.