the-distributive-property MCQs for UPSC Prelims

26 practice questions on the-distributive-property from the We Distribute, Yet Things Multiply section of the UPSC Prelims syllabus. 26 come with a written explanation. Try the sample set below - the answer stays hidden until you ask for it.

8 Easy 13 Medium 5 Hard

Sample questions

Q1
medium

What is the quickest correct mental method for $7 \times 99$?

  1. A $7 \times 100 - 1 = 699$
  2. B $7 \times 90 + 9 = 639$
  3. C $7 \times 100 - 7 = 693$
  4. D $7 \times 100 + 7 = 707$
Show answer and explanation

Correct answer: C - $7 \times 100 - 7 = 693$

Since $99 = 100 - 1$, the product is $700 - 7 \times 1 = 693$. Subtracting only $1$ forgets to multiply the correction, the third option leaves the $9$ unmultiplied, and the last adds where it should subtract.

Q2
medium

Which single product equals $9 \times 25 + 9 \times 15$?

  1. A $9 + 40$
  2. B $9 \times 40$
  3. C $18 \times 40$
  4. D $9 \times 375$
Show answer and explanation

Correct answer: B - $9 \times 40$

The common factor $9$ can be taken out, leaving $9 \times (25 + 15) = 9 \times 40 = 360$. Multiplying $25$ by $15$ is wrong because the two products are added, not multiplied, doubling the $9$ counts the factor twice, and the last option drops the multiplication.

Q3
hard

A trader sells $98$ packets of tea at ₹$45$ each. Which calculation gives the correct total?

  1. A $45 \times 100 - 2 = 4498$
  2. B $45 \times 100 + 45 \times 2 = 4590$
  3. C $45 \times 100 - 45 \times 2 = 4410$
  4. D $45 \times 90 + 45 \times 2 = 4140$
Show answer and explanation

Correct answer: C - $45 \times 100 - 45 \times 2 = 4410$

Writing $98$ as $100 - 2$ gives $4500 - 90 = 4410$, and $45 \times 98$ is indeed ₹$4410$. The second subtracts $2$ rather than $2$ lots of ₹$45$, the third adds the correction instead of subtracting it, and the fourth splits $98$ as $90 + 2$, which is only $92$.

Q4
easy

Which of these writes $4 \times 37$ as a sum of two products?

  1. A $4 + 30 \times 7$
  2. B $4 \times 30 + 4 \times 7$
  3. C $4 \times 30 + 7$
  4. D $4 \times 3 + 4 \times 7$
Show answer and explanation

Correct answer: B - $4 \times 30 + 4 \times 7$

Splitting $37$ into $30 + 7$ and multiplying each part by $4$ gives $120 + 28 = 148$, which is $4 \times 37$. The second leaves the $7$ unmultiplied, the third changes the operations, and the fourth uses $3$ in place of $30$.

Q5
medium

Assertion (A): $7 \times 14$ can be worked out as $7 \times 10 + 7 \times 4$. Reason (R): A rectangle $7$ units by $14$ units can be cut into a $7$ by $10$ rectangle and a $7$ by $4$ rectangle, and the two areas add up to the whole.

  1. A Both A and R are true, and R is the correct explanation of A
  2. B Both A and R are true, but R is not the correct explanation of A
  3. C A is true, but R is false
  4. D A is false, but R is true
Show answer and explanation

Correct answer: A - Both A and R are true, and R is the correct explanation of A

Both sides of A equal $98$, and the cut described in R really does split the rectangle into those two pieces with no overlap and nothing left out. The picture is exactly why the split of the product works, so R explains A.

Q6
easy

Two claims are made about $7 \times (50 - 1)$. (I) It equals $7 \times 50 - 7 \times 1$. (II) It equals $7 \times 50 - 1$. Which is correct?

  1. A Neither (I) nor (II)
  2. B Only (I)
  3. C Both (I) and (II)
  4. D Only (II)
Show answer and explanation

Correct answer: B - Only (I)

The product is $7 \times 49 = 343$. Claim (I) gives $350 - 7 = 343$, so it holds. Claim (II) leaves the $1$ unmultiplied and gives $349$, so it fails. Exactly one of the two is right.

Q7
easy

Which expression is equal to $8 \times (10 - 2)$?

  1. A $8 \times 10 - 2$
  2. B $8 \times 10 - 8 \times 2$
  3. C $8 - 10 \times 2$
  4. D $8 \times 10 + 8 \times 2$
Show answer and explanation

Correct answer: B - $8 \times 10 - 8 \times 2$

The outside factor multiplies both terms and the minus sign is kept, giving $80 - 16 = 64$, which is $8 \times 8$. The second option forgets to multiply the $2$, the third changes the sign, and the fourth rearranges the numbers entirely.

Q8
hard

Ramesh buys $14$ notebooks costing ₹$23$ each and $14$ pens costing ₹$17$ each. Which single multiplication gives his total bill?

  1. A $14 \times 23 \times 17$
  2. B $14 \times 40$
  3. C $14 + 40$
  4. D $28 \times 40$
Show answer and explanation

Correct answer: B - $14 \times 40$

The bill is $14 \times 23 + 14 \times 17$, and taking out the common $14$ leaves $14 \times (23 + 17) = 14 \times 40 = 560$. Multiplying the two prices has no meaning here, doubling the $14$ counts every item twice, and the last option abandons multiplication altogether.

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