Examius
🇮🇳 CAT (Common Admission Test) · flashcards
CAT (Common Admission Test) Quantitative Aptitude (QA) - Arithmetic Flashcards
50 question-and-answer cards covering Quantitative Aptitude (QA) - Arithmetic as it is examined in CAT (Common Admission Test). 24 of them are printed below, taken from across the deck — no signup, no paywall on the preview.
24 sample cards from the Quantitative Aptitude (QA) - Arithmetic deck
Sampled from the end of the deck, so these are different cards from the ones shown on the syllabus page.
What is the difference between ratio and proportion?
A ratio (a:b) compares two quantities. A proportion is an equality of two ratios (a:b = c:d), meaning a x d = b x c (product of extremes = product of means).
In a proportion a:b = c:d, what are componendo and dividendo?
Componendo: (a+b)/b = (c+d)/d. Dividendo: (a-b)/b = (c-d)/d. Componendo-Dividendo: (a+b)/(a-b) = (c+d)/(c-d).
What is the mean proportional (geometric mean) between a and b?
Mean proportional = sqrt(a x b). It is the value x such that a:x = x:b.
Define direct, inverse, and joint variation.
Direct: y = kx (y increases as x increases). Inverse: y = k/x (y decreases as x increases). Joint: y varies with the product/combination of multiple variables, e.g., y = kxz.
In a partnership, how is profit shared when partners invest different amounts for different time periods?
Profit is shared in the ratio of (capital x time) for each partner. E.g., if A invests Pa for Ta and B invests Pb for Tb, ratio = Pa.Ta : Pb.Tb.
What is the difference between a working partner and a sleeping partner?
A working partner manages the business and may receive a salary/commission before profit division. A sleeping (dormant) partner only invests capital and shares profit per the capital-time ratio.
What is the rule of alligation (alligation rule)?
(Cheaper quantity)/(Dearer quantity) = (Dearer price - Mean price)/(Mean price - Cheaper price). It finds the ratio in which two ingredients at different prices are mixed to get a desired mean price.
In a vessel with x litres of pure liquid, after removing y litres and replacing with water n times, what remains?
Remaining pure liquid = x(1 - y/x)^n. This is the repeated-replacement formula.
What is the formula for simple average (arithmetic mean)?
Average = (Sum of all observations)/(Number of observations). Sum = Average x Number of observations.
What is the weighted average formula?
Weighted average = (w1.x1 + w2.x2 + ... + wn.xn)/(w1 + w2 + ... + wn), where wi are weights and xi are values.
How does the average change when a new value is added or removed?
If a value greater than the current average is added, the average rises; if smaller, it falls. New sum = old sum +/- the value; recompute average with the new count.
Define the three measures of central tendency: mean, median, and mode.
Mean = arithmetic average. Median = middle value when data is ordered (average of two middle values if even count). Mode = most frequently occurring value.
What is the empirical relationship between mean, median, and mode?
Mode = 3 x Median - 2 x Mean (approximately, for moderately skewed distributions).
What are the main measures of dispersion?
Range, Quartile Deviation, Mean Deviation, Variance, and Standard Deviation. They measure how spread out the data is around a central value.
What is the formula for standard deviation and variance?
Variance = (1/n) x Sum of (xi - mean)^2. Standard Deviation (SD) = sqrt(Variance). SD has the same units as the data.
What is the coefficient of variation and what does it measure?
Coefficient of Variation (CV) = (Standard Deviation / Mean) x 100%. It measures relative variability and allows comparison of dispersion between datasets with different means/units.
What is the fundamental relationship between speed, distance, and time, and key unit conversions?
Speed = Distance/Time. To convert km/h to m/s, multiply by 5/18; to convert m/s to km/h, multiply by 18/5.
What is the formula for relative speed in same-direction and opposite-direction motion?
Opposite directions: relative speed = sum of speeds (s1 + s2). Same direction: relative speed = difference of speeds (s1 - s2).
What is the average speed for a round trip covering equal distances at speeds a and b?
Average speed = 2ab/(a+b) (the harmonic mean), NOT the arithmetic mean of the two speeds.
How long does a train of length L take to cross a platform of length P at speed v?
Time = (L + P)/v. To cross a pole/point object, time = L/v (only the train's length matters).
In a race, what do 'a beats b by x metres' and 'a beats b by t seconds' mean?
'Beats by x metres' means when A finishes, B is x metres behind. 'Beats by t seconds' means A finishes t seconds before B. A 'start of x metres' means B begins x metres ahead.
On a circular track of length L, when do two runners starting together (same point) first meet, in same and opposite directions?
Same direction: time = L/(s1 - s2). Opposite directions: time = L/(s1 + s2). Time to meet again at the starting point = LCM of (L/s1, L/s2).
If A completes a work in 'a' days and B in 'b' days, how long do they take together?
Combined time = ab/(a+b) days. (Their combined one-day work = 1/a + 1/b.)
What is the formula relating men, days, hours, and work (work equivalence)?
(M1 x D1 x H1)/W1 = (M2 x D2 x H2)/W2, where M = number of workers, D = days, H = hours/day, W = amount of work. This is the chain rule of work.
What this deck covers
The Quantitative Aptitude (QA) - Arithmetic deck follows the CAT (Common Admission Test) Quantitative Aptitude (QA) - Arithmetic syllabus — 5 chapters and 19 topics — so questions land on material that is genuinely examinable rather than trivia around it. That works out to roughly 10.0 cards per chapter.
Answers are written to be recallable, not just readable — averaging about 130 characters, which is long enough to carry the reasoning and short enough to say out loud.
A deck like this earns its keep on the second and third pass. Read the syllabus first so you know the shape of the subject, then use the cards to find the specific facts that have not stuck.
Quantitative Aptitude (QA) - Arithmetic flashcards FAQ
How many Quantitative Aptitude (QA) - Arithmetic flashcards are in this CAT (Common Admission Test) deck?
50 cards. This page previews 24 of them, sampled evenly across the deck so you can judge the difficulty before installing anything.
Are these CAT (Common Admission Test) flashcards free?
Yes. The preview here is free to read with no signup, and the full 50-card deck is free inside the Examius app.
What do the Quantitative Aptitude (QA) - Arithmetic cards cover?
They follow the CAT (Common Admission Test) Quantitative Aptitude (QA) - Arithmetic syllabus — 5 chapters and 19 topics — so the questions track what is actually examinable.
How should I use these flashcards?
Read the syllabus first so you know the shape of the subject, then drill the deck. Examius schedules each card with spaced repetition, so cards you keep missing come back sooner and ones you know drift further apart.