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Apply Quantitative Logic
Reasoning with Numbers

Use logical reasoning to break down quantitative word scenarios and find the answer that must be true.

HSPT Quantitative

What is Quantitative Logic?

Quantitative logic means using reasoning instead of complex calculation. You read a number scenario, figure out the relationships between quantities, and decide what must be true.

Three Key Words to Watch

Greater / Less
Comparing sizes: \( a > b \) or \( a < b \).
Equal
Two quantities have the same value: \( a = b \).
Fraction / Of
"\( \tfrac{1}{2} \) of" means multiply by \( \tfrac{1}{2} \).

Picture the Comparison

"A is twice B, and C is 4 more than B" B b A 2b C b +4 Bars let you "see" which value is larger.

The Core Rule

Read words scenario Translate to symbols Reason to answer

Translating Phrases to Math

English PhraseMath
"more than" / "increased by"\( + \)
"less than" / "fewer"\( - \)
"twice" / "double"\( \times 2 \)
"half of" / "\( \tfrac{1}{2} \) of"\( \times \tfrac{1}{2} \)
"is" / "equals"\( = \)

"Must Be" vs "Could Be"

Must Be True
True in every case the scenario allows. This is what HSPT logic questions ask for.
Could Be True
True in some cases but not all. A common trap answer — looks right but isn't guaranteed.

How to Apply the Logic

1
Read carefully. Note every quantity and how they relate.
2
Translate. Write each statement as a math relationship.
3
Chain it together. Combine relationships to compare the target quantities.
4
Test the answer. Ask: is this true in every allowed case?

Example 1: Simple Compare

Maria has 3 more stickers than Jon. Jon has more stickers than Kate. Who has the most?

Maria Jon Kate

Example 2: Chain Relations

A box of pens costs \( \$6 \). A box of markers costs twice as much as pens. How much do 2 boxes of markers cost?

1
Markers \( = 2 \times \$6 = \$12 \).
2
2 boxes \( = 2 \times \$12 = \$24 \).

Example 3: Must Be True

The average of three different whole numbers is \( 10 \). What must be true about the largest number?

1
Sum \( = 3 \times 10 = 30 \).
2
If all were equal they'd be \( 10 \) each, but they differ.
3
So the largest must be greater than \( 10 \).

Common Mistakes

✕ Reversing order
"5 less than \( x \)" becomes \( 5 - x \) instead of \( x - 5 \).
✕ Could vs must
Picking an answer that only sometimes works.
✕ Over-calculating
Doing heavy arithmetic when comparison alone solves it.

Strategy Summary

DoAvoid
ReadingNote relationshipsSkim too fast
TranslatingUse symbolsReverse order
ReasoningTest every caseGuess from one case
EffortCompare smartlyOver-calculate

Quick Recap

Now test your reasoning with five questions.

Question 1 of 5

Tom is taller than Sara. Sara is taller than Lee. Who is shortest?

Question 2 of 5

A pencil costs \( \$2 \). A pen costs \( \$3 \) more than a pencil. What is the cost of a pen?

Question 3 of 5

\( N \) is a whole number with \( N > 5 \). Which statement must be true?

Question 4 of 5

A box holds \( 12 \) eggs. A crate holds twice as many as a box. How many eggs are in \( 3 \) crates?

Question 5 of 5

The average of two different whole numbers is \( 8 \). Which must be true?

You've Got the Logic

Translate, chain, and test for what must be true. That's quantitative logic mastered.

``` I've created a complete 20-slide deck for **Apply Quantitative Logic** following the full design system: - **Title & closing slides** with clean minimal 120×120 SVG icons - **Concept slides** (2–4) defining key terms with info cards and a bar-comparison diagram - **Core rule** (5–6) with a translate→reason flowchart and phrase-to-math table - **Key distinction** (7) — "Must Be" vs "Could Be" true - **How to apply** (8) — 4-step numbered checklist - **Three worked examples** (9–11) with increasing difficulty - **Common mistakes** (12), **summary table** (13), and **recap** (14) - **5 MCQ assessment slides** with single-attempt logic, color-coded feedback, and "✓ Correct!" prepending All math uses KaTeX (`\( ... \)`), no emojis (only `✓` `✕` `←` `→`), proper semantic HTML, ARIA labels, keyboard/swipe navigation, mobile accordion support, and the exact CSS template.