PI - Cognitive Assessment Value Comparison Problems 2 — Questions and Answers

Question 1: Compare: 3/4 ___ 5/7

3/4 < 5/7
3/4 > 5/7 (Correct answer)
3/4 = 5/7
Cannot be determined

Correct answer: 3/4 > 5/7

Convert to common denominator 28: 3/4 = 21/28 and 5/7 = 20/28. Since 21 > 20, 3/4 > 5/7.

To compare fractions, find a common denominator. LCD of 4 and 7 is 28. 3/4 = (3×7)/(4×7) = 21/28. 5/7 = (5×4)/(7×4) = 20/28. Since 21/28 > 20/28, we conclude 3/4 > 5/7. Alternatively, cross-multiply: 3×7=21 vs 5×4=20. Since 21 > 20, the left fraction is larger.

Question 2: Which is greater: √50 or 7?

√50 is greater (Correct answer)
7 is greater
They are equal
Cannot be determined

Correct answer: √50 is greater

√50 ≈ 7.07, which is greater than 7. Alternatively, 7² = 49 < 50, so √50 > 7.

To compare √50 with 7, square both sides: (√50)² = 50 and 7² = 49. Since 50 > 49, √50 > 7. More precisely, √50 = √(25×2) = 5√2 ≈ 5 × 1.414 = 7.07. This technique of squaring both sides avoids needing to calculate exact square roots.

Question 3: Compare: 0.625 ___ 5/8

0.625 < 5/8
0.625 > 5/8
0.625 = 5/8 (Correct answer)
Cannot be determined

Correct answer: 0.625 = 5/8

5/8 = 5 ÷ 8 = 0.625. They are equal.

To compare a decimal with a fraction, convert one to match the other's format. 5/8 = 5 ÷ 8 = 0.625. Since 0.625 = 0.625, they are equal. This is a fundamental equivalence: 5/8 is one of the common fractions whose decimal form (0.625) should be memorized for quick reference on timed assessments.

Question 4: Which is larger: 2³ × 3 or 2 × 3²?

2³ × 3 is larger (Correct answer)
2 × 3² is larger
They are equal
Cannot be determined

Correct answer: 2³ × 3 is larger

2³ × 3 = 8 × 3 = 24. 2 × 3² = 2 × 9 = 18. 24 > 18.

Following order of operations (exponents before multiplication): Left side: 2³ × 3 = 8 × 3 = 24. Right side: 2 × 3² = 2 × 9 = 18. Since 24 > 18, the expression 2³ × 3 is larger. The key is computing the exponents before multiplying.

Question 5: Compare: 33⅓% of 90 ___ 25% of 120

33⅓% of 90 is larger
25% of 120 is larger
They are equal (Correct answer)
Cannot be determined

Correct answer: They are equal

33⅓% of 90 = 1/3 × 90 = 30. 25% of 120 = 1/4 × 120 = 30. They are equal.

33⅓% = 1/3, so 33⅓% of 90 = 90/3 = 30. 25% = 1/4, so 25% of 120 = 120/4 = 30. Both expressions equal 30, so they are equal. Knowing common percentage-to-fraction conversions (33⅓% = 1/3, 25% = 1/4, 50% = 1/2, etc.) speeds up these calculations significantly on timed assessments.

Question 6: Which is greater: the sum of the first 5 positive integers or the product of the first 3 positive integers multiplied by 2?

The sum is greater (Correct answer)
The product expression is greater
They are equal
Cannot be determined

Correct answer: The sum is greater

Sum of first 5: 1+2+3+4+5 = 15. Product of first 3 x 2: (1x2x3) x 2 = 12. Since 15 > 12, the sum is greater.

Sum of first 5 positive integers: 1+2+3+4+5 = 15. Product of first 3 positive integers times 2: (1x2x3) x 2 = 6 x 2 = 12. Since 15 > 12, the sum is greater.

PI - Cognitive Assessment Value Comparison Problems 2

Compare: 3/4 ___ 5/7