Quantitative Aptitudeमात्रात्मक योग्यता · सरलीकरण और सन्निकटन
Simplification and Approximationसरलीकरण और सन्निकटनquestions and answersप्रश्न और उत्तर
Simplification and approximation are pure speed marks. In bank prelims they can be five or more questions, so fluency here is worth a lot.
Unlimitedअसीमितfresh questionsनए प्रश्न
Answersउत्तरalways one tap awayहमेशा एक टैप दूर
2subtopicsउप-टॉपिक
SSC CGL ~2
IBPS PO ~5
Practice questions are in English for now.अभ्यास के प्रश्न अभी अंग्रेज़ी में हैं।
How simplification and approximation worksसरलीकरण और सन्निकटन को समझिए
BODMAS: brackets first, then “of”, then division and multiplication from left to right, then addition and subtraction from left to right.
In approximation questions the options are far apart. Round every number to something easy (for example 49.8% → 50%, 1999 → 2000), compute, and choose the nearest option.
Train your tables, squares and fraction values: the Aptitude Gym drills exactly these.
Each trick says when to use it, why it works and when it fails. Formula tricks are checked by code over their whole range.हर ट्रिक बताती है कि उसे कब इस्तेमाल करें, वह क्यों काम करती है और कब नहीं। सूत्र वाली ट्रिक्स को कोड से उनकी पूरी रेंज पर जाँचा गया है।
Option killerविकल्प-छँटनीRarely taughtकम सिखाई जाने वाली✓ Checked on 6,560 cases✓ 6,560 मामलों पर जाँची गई
Option killer: the digit-sum check
Use it when:कब इस्तेमाल करें: Exact multiplication, addition or subtraction questions where all the options are close.
Reduce each number to its digit sum, repeating until one digit (4,327 → 16 → 7).
Do the same operation on these single digits and reduce again.
The correct option must have the same digit sum. Usually only one does.
Why it works, and when it failsयह क्यों काम करती है, और कब नहीं
Why:क्यों: A number and its digit sum leave the same remainder when divided by 9, and remainders survive addition, subtraction and multiplication (“casting out nines”).
Limits:सीमाएँ: Cannot tell apart options that differ by a multiple of 9, and does not work for division or decimals. Pair it with the last-digit check.
Option killerविकल्प-छँटनीRarely taughtकम सिखाई जाने वाली✓ Checked on 18,172 cases✓ 18,172 मामलों पर जाँची गई
Option killer: the last-digit check
Use it when:कब इस्तेमाल करें: Products, squares or sums where the options end in different digits.
Multiply (or add) only the last digits of the numbers.
Keep the last digit of that result; strike out every option that ends differently.
Why it works, and when it failsयह क्यों काम करती है, और कब नहीं
Why:क्यों: For products and quotients, relative errors add: (1 + e₁)(1 + e₂) ≈ 1 + e₁ + e₂. Opposite roundings have opposite signs and cancel.
Limits:सीमाएँ: When options are within 2–3% of each other, calculate exactly (and use the digit-sum check).
Mental mathsमानसिक गणित✓ Checked on 1,485 cases✓ 1,485 मामलों पर जाँची गई
x% of y = y% of x
Use it when:कब इस्तेमाल करें: An awkward percentage of a friendly number, such as 16% of 25 or 8% of 50.
Swap the two numbers.
16% of 25 becomes 25% of 16 = 4.
Exampleउदाहरण
18% of 50
→ 50% of 18 = 9
Why it works, and when it failsयह क्यों काम करती है, और कब नहीं
Why:क्यों: x/100 × y = y/100 × x, because multiplication is commutative.
Limits:सीमाएँ: Always true; it only helps when one of the two numbers is a friendly percentage (10, 20, 25, 50…).
Mental mathsमानसिक गणित✓ Checked on 598 cases✓ 598 मामलों पर जाँची गई
Square from a neighbour you know
Use it when:कब इस्तेमाल करें: Squaring a number next to one you already know (41, 49, 51, 99).
n² = (n − 1)² + (n − 1) + n, or going down: n² = (n + 1)² − (n + 1) − n.
For two numbers equally far from a round one: (a + d)(a − d) = a² − d².
Exampleउदाहरण
41² and 47 × 53
→ 1600 + 40 + 41 = 1681; 2500 − 9 = 2491
Why it works, and when it failsयह क्यों काम करती है, और कब नहीं
Why:क्यों: n² − (n − 1)² = 2n − 1 = (n − 1) + n, and (a + d)(a − d) = a² − d².
Limits:सीमाएँ: Always true; it is fastest when the neighbour is a round number.
Mental mathsमानसिक गणित✓ Checked on 8,640 cases✓ 8,640 मामलों पर जाँची गई
Compare two ratios without dividing
Use it when:कब इस्तेमाल करें: DI questions like “in which year was the ratio highest?” or “which is greater, 37/53 or 41/59?”.
a/b > c/d exactly when a × d > b × c (for positive numbers).
For growth rates, compare (new/old) the same way: no percentages needed.
Exampleउदाहरण
37/53 or 41/59?
→ 37 × 59 = 2,183 and 53 × 41 = 2,173, so 37/53 is bigger.
Why it works, and when it failsयह क्यों काम करती है, और कब नहीं
Why:क्यों: Multiplying both sides of a/b > c/d by the positive number b·d keeps the inequality and removes the division.
Limits:सीमाएँ: Positive numbers only; with negative values the direction can flip.
Mental mathsमानसिक गणित✓ Checked on 999 cases✓ 999 मामलों पर जाँची गई
Square root of a perfect square: unit digit, bracket, then the “5” test
Use it when:कब इस्तेमाल करें: The square root of a perfect square of up to six digits is asked, or an option must be checked as a square.
Last digit → possible last digits of the root: 1 → 1/9, 4 → 2/8, 9 → 3/7, 6 → 4/6, 5 → 5, 0 → 0.
Strike off the last two digits; find the largest square not more than what is left. Its root gives the leading digit(s).
If two candidates remain, compare the number with the square of the middle one ending in 5: below it → the smaller candidate, above it → the larger.
Exampleउदाहरण
√7,056
→ Ends in 6 → 4 or 6. 70 lies between 8² and 9² → 84 or 86. 85² = 7,225 > 7,056 → 84.
Why it works, and when it failsयह क्यों काम करती है, और कब नहीं
Why:क्यों: A square’s last digit depends only on the root’s last digit, and (10t)² ≤ N < (10t + 10)² pins down the leading part t. Between 10t + d and 10t + 10 − d, the square of 10t + 5 lies in the middle, so the comparison picks the right one.
Limits:सीमाएँ: Only for exact perfect squares. A non-square ending in 1, 4, 5, 6, 9 or 0 still gives a confident but wrong answer, so check by squaring when in doubt.
Solved examplesहल किए गए उदाहरण
Answers and full solutions are shown. Hide them to test yourself first.उत्तर और पूरे हल दिखाए गए हैं। पहले खुद को परखने के लिए इन्हें छिपाइए।
Example 1उदाहरण 1 · Simplification (BODMAS) · Easyआसान