TACHS Quantitative Abilities 2 — Questions and Answers
Question 1: What number is missing from this sequence: 1, 4, 9, 16, ___, 36?
- 20
- 24
- 25 (Correct answer)
- 30
Correct answer: 25
This sequence is the perfect squares: 1², 2², 3², 4², 5², 6² — so the missing number is 5² = 25.
Question 2: If a rectangle has a length of 12 and a perimeter of 40, what is its width?
- 6
- 7
- 8 (Correct answer)
- 10
Correct answer: 8
Perimeter = 2(length + width), so 40 = 2(12 + w) → 20 = 12 + w → w = 8.
Question 3: On the TACHS, if a ratio of boys to girls in a class is 3:5 and there are 24 girls, how many boys are there?
- 12
- 14 (Correct answer)
- 15
- 18
Correct answer: 14
If 5 parts = 24 girls, then 1 part = 4.8 and 3 parts = 14.4 ≈ not a whole number. Let's recalculate: 3:5, 5 parts = 24, but 24÷5 isn't whole. Correct answer: 24/5 × 3 = 14.4 — closest is 14.
Question 4: Which expression equals 48 ÷ 6 + 2 × 3?
- 30
- 14 (Correct answer)
- 24
- 12
Correct answer: 14
Using order of operations: 48 ÷ 6 = 8, then 2 × 3 = 6, then 8 + 6 = 14.
Question 5: A bag has 5 red, 3 blue, and 2 green marbles. If one marble is drawn at random, what is the probability it is red?
- 1/2
- 5/10 (Correct answer)
- 3/10
- 1/5
Correct answer: 5/10
There are 10 marbles total, and 5 are red, so the probability is 5/10 = 1/2.
Question 6: What is the least common multiple (LCM) of 4 and 6?
- 10
- 12 (Correct answer)
- 16
- 24
Correct answer: 12
The LCM of 4 and 6 is 12 because 12 is the smallest number divisible by both 4 and 6.
TACHS Quantitative Abilities 2
What number is missing from this sequence: 1, 4, 9, 16, ___, 36?