GRE General Test · GRE & GMAT Analytical Reasoning
GMAT Quantitative Reasoning
Problem-solving in arithmetic and elementary algebra without data sufficiency.
Six concepts. GMAT Focus Quantitative Reasoning is multiple-choice arithmetic and elementary algebra with no calculator — so the marks sit in clean setups, estimation, and answer-choice tactics as much as in the algebra itself.
- GRE General Test
- Medium level
- 6 concepts
- 5 practice questions
1No calculator: estimate before you grind
The GMAT Focus Quant section allows no calculator, so mental math, estimation, and efficient setups are essential. Exact arithmetic still matters, but the first move is a rough size check that kills options you will never need to compute fully.
Round to friendly neighbours, multiply, and ask which choices survive. Only then spend time on the exact product or the last digit. Estimation is not a guess — it is a filter that makes the remaining arithmetic shorter.
Figure. No calculator: estimate to kill choices, then compute only what remains. Grinding the exact product first is the slow path.
How to estimate first
- Round to friendsPush each factor to a nearby multiple of 10 or 5 so the product is mental.
- Size the answerUse that product to discard choices that are obviously too big or too small.
- Finish exactlyCompute the surviving neighbourhood — difference of squares, a last digit, or one careful multiplication.
48 × 52 without a grind
Which value is closest to 48 \times 52? (A) 2400 (B) 2496 (C) 2600 (D) 2704
- Round both toward 50: 50 \times 502500
- Choices far from 25002400 and 2704 out
- Exact: (50-2)(50+2) = 50^2 - 2^22500 − 4 = 2496
- Closest listed value2496
Pro tip. Difference of squares is the exact finish once estimation has told you the answer lives near 2500. Estimate first to eliminate; then pick the identity that finishes in one line.
Before computing exactly, 19 \times 21 is closest to
- 300
- 400
- 500
Round to 20 \times 20 = 400. Exact is 399, so 400 is the right neighbourhood; 300 and 500 are the traps from rounding only one factor or sliding a place value.
2What Focus Quant actually tests
Focus Quant tests arithmetic, number properties, and algebra — equations, inequalities, exponents — applied to word problems. Geometry is de-emphasized in the Focus edition, so time spent memorising circle theorems is time stolen from rates, percents, and clean algebra.
Read every stem as one of those families. If the stem is a word problem, the content is still arithmetic or algebra wearing a story; translate it rather than inventing a geometric diagram the section barely uses.
Figure. Focus Quant centres arithmetic, number properties, and algebra. Geometry is de-emphasized — do not spend drill time on circle theorems.
How to classify a stem
- Name the familyArithmetic (percents, ratios, rates), number properties (odds/evens, factors), or algebra (equations, inequalities, exponents).
- Ignore the sceneryShirts, trains and machines are packaging — the unknowns are still sums, products and rates.
- Skip geometry muscle memoryUnless the stem truly needs a figure property, do not reach for circle or triangle lore first.
| Family | Typical ask | De-emphasized? |
|---|---|---|
| Arithmetic | Percents, ratios, averages, rates | No |
| Number properties | Factors, odds/evens, signs | No |
| Algebra | Equations, inequalities, exponents | No |
| Geometry | Angles, circles, solid figures | Yes — Focus edition |
On GMAT Focus Quant, which topic family is deliberately de-emphasized?
- Algebraic inequalities
- Geometry
- Percent word problems
Focus Quant still hammers arithmetic and algebra on word problems; geometry is the family the edition de-emphasizes. Inequalities and percent stories remain in scope.
3Translate words into equations carefully
Convert words to equations precisely — "is" means equals, "of" means multiply, "percent" means divide by 100. Most wrong answers on Focus Quant are not arithmetic slips; they are mistranslations that set up the wrong equation and then solve it flawlessly.
Write the equation before you touch a percentage as a decimal. If the sentence has two quantities and a relationship word, that word is an operator — treat it as one.
Figure. Map relation words to operators before any arithmetic. Most Focus Quant misses start as mistranslations, not multiply errors.
How to translate
- Underline operatorsMark is / of / percent / more than / less than before introducing a variable.
- Build the equationReplace each marked word with =, \times, or /100 and leave the unknown as n.
- Solve onceOnly after the equation matches the sentence do you compute.
"Increased by 20% of itself"
A number increased by 20% of itself equals 84. What is the number?
- Translate: n + 0.20n = 841.20n = 84
- n = 84 / 1.2070
- Check: 70 + 0.20\times7070 + 14 = 84
- The number70
Pro tip. "Increased by 20% of itself" is 1.2n, not n+20. If you add 20 as a raw count you have ignored "percent" and "of" in the same sentence.
In a translation, "30% of 50" becomes
- 30 + 50
- 30/50
- (30/100)\times 50
"Percent" is /100 and "of" is multiply, so (30/100)\times 50 = 15. Adding treats "of" as unused; dividing reverses the operators.
4Back-solve from the middle choice
Because Focus Quant is multiple-choice, back-solving from the options and plugging in numbers are powerful shortcuts. When direct algebra is slow, start with the middle choice — on a five-option item that is usually (C) — and move up or down with the inequality the stem gives you.
Back-solving is not a guess. Each trial is a full substitution that either satisfies the stem or tells you which direction the true answer lies.
Figure. Three consecutive integers sit one apart; their average is the middle bar. When the sum is 72, that middle is 24 and the largest is the bar one step above it.
How to back-solve
- Start mid-packTest the middle listed value first so one failure tells you which side remains.
- Substitute fullyPlug the trial into the stem's condition — sum, product, or inequality — not into a rewritten hope.
- Walk toward truthIf the trial is too small or too large, step one choice in that direction and stop at the first that fits.
Three consecutive integers
The sum of three consecutive integers is 72. What is the largest? (A) 23 (B) 24 (C) 25 (D) 26 (E) 27
- Average = middle integer = 72/324
- Integers around the middle23, 24, 25
- Largest25
- Verify 23+24+2572 — choice (C)
Pro tip. For consecutive-integer sums, the middle term equals the average; then read off the largest. Back-solving from (C)=25 recovers the same triple in one substitution if you prefer testing choices over naming the middle first.
Three consecutive integers sum to 51. The largest is
- 16
- 17
- 18
Middle = 51/3 = 17, so the integers are 16, 17, 18 and the largest is 18. Picking 17 answers the middle; picking 16 answers the smallest.
5Pick smart numbers (often 100)
Pick smart numbers like 100 for percentage problems to keep arithmetic clean without a calculator. When the stem is about percents or ratios and never names a concrete starting value, you are free to choose one — and 100 turns every percent into a whole number.
The chosen number must respect every constraint in the stem. If a quantity must stay positive, or a rate must be an integer of hours, pick a value that keeps every intermediate integer too.
Figure. With start 100, the +25% bar reaches 125 and the −20% bar returns to 100. The dashed rule is the start line the net change is measured against — here the net is zero.
How to pick numbers
- Confirm freedomIf no absolute starting value is fixed, a stand-in is legal.
- Choose 100 for percentsA 25% rise on 100 is +25, not a decimal grind.
- Run the storyApply each change to your stand-in and read the net as a percent of 100.
Successive percent changes on 100
A price rises by 25% and then falls by 20%. What is the net percent change?
- Pick start = 100100
- After +25%: 100 \times 1.25125
- After −20%: 125 \times 0.80100
- Net change from 1000%
Pro tip. 100 makes the trap visible: +25 then −20 lands exactly back at the start, so the net is 0%, not +5%. Adding the percents is the error the smart number was chosen to expose.
Using a start of 100, a 10% rise then a 10% fall ends at
- 100
- 99
- 98
100 \times 1.10 = 110, then 110 \times 0.90 = 99. Equal-size rise and fall do not cancel; the fall acts on a larger base.
6Chain percent changes by multiplying factors
A markup and a discount are two successive percent changes on different bases. Convert each change to a factor — +25% is ×1.25, −10% is ×0.90 — and multiply. Never add the percents and call that the net; the second percent acts on the marked price, not on cost.
Profit is still revenue minus cost at the end. The factor product tells you the selling price; subtract cost only when the question asks for profit rather than price.
Figure. Cost 40 rises to marked 50 (\times 1.25), then falls to selling 45 (\times 0.90). The selling bar is above cost — net factor 1.125 — even though a discount followed the markup.
How to chain percents
- Write each factorIncrease a\% → \times(1+a/100); decrease b\% → \times(1-b/100).
- Multiply in orderApply markup before discount when the story marks up first.
- Read net from the productA product of 1.125 means 12.5\% above the start — not 15\%.
Markup then discount on a shirt
A shirt is marked up 25% over its $40 cost, then sold at a 10% discount off the marked price. What is the selling price?
- Marked price = 40 \times 1.25$50
- Selling price = 50 \times 0.90$45
- Net factor = 1.25 \times 0.901.125
- Net vs cost12.5% above cost
Pro tip. Chain percentage changes by multiplying factors; never add 25% and −10% directly. The factor product is the whole answer when the question asks for selling price or net percent.
Cost $60, marked up 20%, then 10% off the marked price. Selling price is
- $64.80
- $66
- $72
60 \times 1.20 = 72, then 72 \times 0.90 = 64.80. $66 adds +20 and -10 as points on 60; $72 stops after the markup.
Notes
- No Calculator: The GMAT Focus Quant section allows no calculator, so mental math, estimation, and efficient setups are essential.
- Content Scope: It tests arithmetic, number properties, and algebra (equations, inequalities, exponents) applied to word problems—geometry is de-emphasized in the Focus edition.
- Answer-Choice Strategy: Since it is multiple-choice, back-solving from the options and plugging in numbers are powerful shortcuts.
- Translate Carefully: Convert words to equations precisely—'is' means equals, 'of' means multiply, 'percent' means divide by 100.
Formulas
- Distance-rate-time: d = r\cdot t
- Percent: \text{part} = \dfrac{\%}{100}\times \text{whole}
- Average: \dfrac{\text{sum}}{\text{count}}
- Combined work rate: \dfrac{1}{t} = \dfrac{1}{t_1}+\dfrac{1}{t_2}
- Profit: \text{Profit} = \text{Revenue} - \text{Cost}
Exam traps & shortcuts
- Back-solve by testing answer choices (start with the middle value) when direct algebra is slow.
- Pick smart numbers like 100 for percentage problems to keep arithmetic clean without a calculator.
- Estimate first to eliminate obviously wrong choices before doing exact computation.
Reference tables
The relations Focus Quant keeps returning to. Each line should be rebuildable from a word problem, not only recalled.
| Quantity | Relation | Watch for |
|---|---|---|
| Distance–rate–time | d = r\cdot t | Match units before multiplying |
| Percent of a whole | \text{part} = (\%/100)\times\text{whole} | "Of" multiplies; convert % first |
| Average | \text{sum}/\text{count} | Weighted averages need weights |
| Combined work | 1/t = 1/t_1 + 1/t_2 | Rates add; times do not |
| Profit | \text{Profit} = \text{Revenue} - \text{Cost} | Selling price is not profit |
The translation dictionary from the translate-carefully concept, gathered for drill.
| English | Operator | Example fragment |
|---|---|---|
| is / are / equals | = | "x is 12" → x=12 |
| of | \times | "20% of 50" → 0.2\times50 |
| percent | /100 | "25 percent" → 25/100 |
| more than | + on the base | "5 more than n" → n+5 |
| less than | order flips | "5 less than n" → n-5 |
Recap
Read only this the night before a Focus Quant section.
- No calculator
- Estimate to a friendly neighbourhood first; finish with an identity or one exact product.
- Scope
- Arithmetic, number properties, algebra on word problems. Geometry is de-emphasized — do not lead with it.
- Translate
- is → =; of → \times; percent → /100. Wrong equation, perfect arithmetic, wrong answer.
- Back-solve
- Start at the middle choice. For consecutive-integer sums, middle = average.
- Smart 100
- When no start value is fixed, pick 100 for percent stories so every step stays integer.
- Chain factors
- Markup then discount multiplies: 1.25\times0.90=1.125, not +15\%. Profit is revenue − cost at the end.
Practise GMAT Quantitative Reasoning
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- 5 exam-style questions on this topic, with explanations
- A 5-question practice set that ends the chapter
- Timed mocks scored with the real marking scheme
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