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CAT (cloned) / Percentages and Variations

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CAT Study Notes: Percentage and Variations

Question

How do you convert a percentage to a decimal?

Answer

Divide the percentage by 100. For example, 25% becomes 0.25.

Question

What is the formula for calculating percentage change?

Answer

Percentage Change = [(New Value - Original Value) / Original Value] × 100.

Question

If an item's cost price is ₹500 and it is sold for ₹600, what is the profit percentage?

Answer

Profit = ₹100. Profit % = (100/500) × 100 = 20%.

Question

A product with a marked price of ₹800 is sold at a 15% discount. What is the selling price?

Answer

Discount = 15% of 800 = ₹120. Selling Price = 800 - 120 = ₹680.

Question

What is the defining equation for direct variation, and how do the variables relate?

Answer

y = kx, where k is a constant. As x increases, y increases proportionally.

Question

What is the defining equation for inverse variation, and how do the variables relate?

Answer

y = k/x, where k is a constant. As x increases, y decreases.

Question

If y varies directly with x and y=10 when x=4, what is y when x=16?

Answer

First, find k: 10 = k*4, so k=2.5. Then, for x=16, y = 2.5 * 16 = 40.

Question

What is the formula for calculating the net effect of two successive percentage changes, a% and b%?

Answer

Net Percentage Change = a + b + (a*b/100). Use '+' for increase and '-' for decrease.

Question

If a quantity increases by 20% and then decreases by 20%, what is the net percentage change?

Answer

Net change = 20 + (-20) + (20*(-20)/100) = 0 - 4 = -4%. There is a net decrease of 4%.

Question

In the context of mixtures, what does the percentage concentration typically represent?

Answer

It represents the proportion of a particular substance (solute) in the total mixture (solute + solvent).

Question

According to the CAT strategy, when should you attempt a percentage problem?

Answer

When it involves straightforward percentage change, profit-loss, discount, or one-step variation problems.

Question

According to the CAT strategy, when should you be cautious or skip a percentage problem?

Answer

With word problems involving multiple layers of percentage changes, reverse calculations, or fake weights without a clear shortcut.

Question

What is the recommended time allocation for a standalone percentage question in the CAT exam?

Answer

Aim for 1-2 minutes per standalone question. In Data Interpretation, aim for sub-30 seconds each using approximation.

Question

What mental math skill is emphasized for percentage calculations in the CAT?

Answer

Memorize fraction-percentage equivalents (e.g., 1/2=50%, 1/4=25%) and practice quickly extracting 10% and 1% of a number.

Question

What is the primary purpose of the 'Alligation rule' mentioned in the study notes?

Answer

The Alligation rule is a shortcut method used to find the ratio in which ingredients at different prices or concentrations must be mixed.

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