We Distribute, Yet Things Multiply MCQs for UPSC Prelims
110 practice questions covering We Distribute, Yet Things Multiply, organised into 1 topics.
110 questions include a written explanation.
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A student writes: Step 1, $2(x + 5) = 2x + 10$; Step 2, $2x + 10 + 3x = 5x + 10$. Where is the mistake?
ABoth steps are wrong
BThere is no mistake; both steps are correct
CStep 1
DStep 2
Show answer and explanation
Correct answer: B - There is no mistake; both steps are correct
Step 1 multiplies both terms by $2$ correctly, and Step 2 combines the like terms $2x$ and $3x$ into $5x$ while leaving the constant alone. Checking with $x = 1$ gives $15$ at every stage, so the working is sound throughout.
Q2
medium
What is the quickest correct mental method for $7 \times 99$?
A$7 \times 90 + 9 = 639$
B$7 \times 100 - 1 = 699$
C$7 \times 100 - 7 = 693$
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.
Q3
medium
Which property allows $(9 \times 4) \times 5$ to be rewritten as $9 \times (4 \times 5)$?
AThe associative property
BThe commutative property
CThe distributive property
DThe identity property
Show answer and explanation
Correct answer: A - The associative property
The three factors stay in the same order and only the brackets move, which is exactly associativity. Commutativity would swap factors, distribution needs a sum or difference inside a bracket, and the identity property is about multiplying by $1$.
Q4
medium
Which single product equals $9 \times 25 + 9 \times 15$?
A$9 + 40$
B$9 \times 40$
C$9 \times 375$
D$18 \times 40$
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.
Q5
medium
You need the value of $4x + 4y$ when $x = 13$ and $y = 12$. Which equivalent form makes this quickest?
A$(4x)(4y)$, since the factor applies to each bracket
B$4x + 4y$ worked term by term, since two multiplications are easy
C$4xy$, since the common factor can be joined to both letters
D$4(x + y)$, since $13 + 12 = 25$ and $4 \times 25 = 100$
Show answer and explanation
Correct answer: D - $4(x + y)$, since $13 + 12 = 25$ and $4 \times 25 = 100$
Taking out the common factor turns two multiplications into one easy one, giving $100$. Working term by term gives the same $100$ but with more effort, while $4xy$ gives $624$ and $(4x)(4y)$ gives $2496$, so neither of those is even equivalent.
Q6
medium
Two expressions give different values when $x = 1$ is substituted. What follows?
AThey are equivalent
BNothing at all can be concluded
CThey are equivalent for every value except $x = 1$
DThey are certainly not equivalent
Show answer and explanation
Correct answer: D - They are certainly not equivalent
Equivalent expressions must agree for every value of the letter, so a single disagreement settles the matter at once. One disagreement cannot prove equivalence, it is certainly informative, and equivalence is never something that fails at just one value.
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