Understanding Integers: MCQ test, Set 9

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Choose one answer for each question, then check your score at the end. Each correct answer carries 1 mark; there is no negative marking.

Starting at $6$ , Anil makes $12$ jumps of $1$ to the left on the number line. Anil lands on
A $-7$ B $-6$ C $-5$ D $18$

Answer and solution

Answer: (B) $-6$

Jumps to the left subtract.

$6 - 12 = -(12 - 6) = -6$
The number of integers between $-10$ and $15$ is
A $5$ B $26$ C $25$ D $24$

Answer and solution

Answer: (D) $24$

Between $-10$ and $0$ : $9$ ; then $0$ itself; between $0$ and $15$ : $14$ .

Total $= 9 + 1 + 14 = 24$
The value of $-77 - 79$ is
A $-156$ B $-2$ C $-46$ D $-166$

Answer and solution

Answer: (A) $-156$

Both are negative: add and keep the $-$ sign.

$-77 - 79 = -(77 + 79) = -156$
The sum of $-98$ and $-64$ is
A $-34$ B $-172$ C $-52$ D $-162$

Answer and solution

Answer: (D) $-162$

Adding $-64$ to $-98$ gives $-98 - 64$ .

Both are negative: $-98 - 64 = -(98 + 64) = -162$
In $-32 + 25 = -(\square)$ , the number in the box is
A $17$ B $13$ C $7$ D $57$

Answer and solution

Answer: (C) $7$

Different signs: subtract the smaller from the bigger; the bigger is negative, so the answer is negative.

$-32 + 25 = -(32 - 25) = -(7)$
$-86 + 69 =$
A $-27$ B $-155$ C $-17$ D $-23$

Answer and solution

Answer: (C) $-17$

Different signs: subtract the smaller from the bigger and keep the sign of the bigger.

$-86 + 69 = -(86 - 69) = -17$
The sum of $47$ and $-83$ is
A $-44$ B $-36$ C $-46$ D $-130$

Answer and solution

Answer: (B) $-36$

This is $47 - 83$ .

$47 - 83 = -(83 - 47) = -36$
A trader gained ₹2663 on one deal and lost ₹3016 on another. Altogether this is
A a profit of ₹353 B a loss of ₹1653 C a loss of ₹353 D a loss of ₹5679

Answer and solution

Answer: (C) a loss of ₹353

Gain $= +2663$ , loss $= -3016$

$2663 - 3016 = -(3016 - 2663) = -353$

A loss of ₹353.
The value of $-8187 + 6189$ is
A $-1998$ B $-14376$ C $-2008$ D $-2002$

Answer and solution

Answer: (A) $-1998$

Different signs: subtract and keep the sign of the bigger number.

$-8187 + 6189 = -(8187 - 6189) = -1998$
Subtract $8574$ from $88101$ . The answer is
A $80637$ B $80473$ C $79527$ D $79528$

Answer and solution

Answer: (C) $79527$

Subtract column by column from the units, borrowing where the top digit is smaller.

$88101 - 8574 = 79527$
Divya worked out $74324 - 3258$ and got $71134$ , which is wrong. The correct answer is
A $71066$ B $71065$ C $71176$ D $71067$

Answer and solution

Answer: (A) $71066$

Subtract column by column from the units. When you borrow, take the $1$ away from the next column.

$74324 - 3258 = 71066$
To find $702 - 494$ , Arjun counts down $702 \to 500 \to 494$ . The two jumps are
A $202$ and $94$ B $202$ and $16$ C $302$ and $6$ D $202$ and $6$

Answer and solution

Answer: (D) $202$ and $6$

$702 \to 500$ : $702 - 500 = 202$

$500 \to 494$ : $500 - 494 = 6$

(So $702 - 494 = 202 + 6 = 208$ .)
$559 - 727 =$
A $-232$ B $-1286$ C $-278$ D $-168$

Answer and solution

Answer: (D) $-168$

$559 - 727 = -(727 - 559)$

$727 \to 600 \to 559$ : $127 + 41 = 168$

So the answer is $-168$
$6012 - 356 - 7607 =$
A $-1951$ B $-1239$ C $-13975$ D $13263$

Answer and solution

Answer: (A) $-1951$

Positive term: $6012$

Negative terms: $356 + 7607 = 7963$

$6012 - 356 - 7607 = 6012 - 7963$ $= -(7963 - 6012) = -1951$
In $714 + 322 - 245 - 43$ , the total of the positive terms and the total of the negative terms (without the sign) are
A $1036$ and $298$ B $714$ and $610$ C $1281$ and $43$ D $1036$ and $288$

Answer and solution

Answer: (D) $1036$ and $288$

Positive terms: $714 + 322 = 1036$

Negative terms: $245 + 43 = 288$
$906 - 15 + 381 - 751 =$
A $2053$ B $-241$ C $551$ D $521$

Answer and solution

Answer: (D) $521$

Add the positive terms, add the negative terms, then subtract.

$906 - 15 + 381 - 751 = 1287 - 766$ $= 521$
Without working it out, the product $-84 \times 42$ is
A zero B negative C positive, because the bigger number decides D positive

Answer and solution

Answer: (B) negative

$- \times + = -$

So the product is negative.
$43 \times -6$ equals
A $-258$ B $-49$ C $-264$ D $37$

Answer and solution

Answer: (A) $-258$

Sign: $+ \times - = -$

$43 \times 6 = 258$ , so $43 \times -6 = -258$
Which of these equals $132$ ?
A $3 - 135$ B $-4 \times -33$ C $-3 \times 44$ D $-78 - 54$

Answer and solution

Answer: (B) $-4 \times -33$

$-4 \times -33$ : $- \times - = +$ , so it is $132$

The others are all $-132$ : $-3 \times 44$ is $- \times +$ , and the two additions give $-(78 + 54)$ and $-(135 - 3)$ .
$-436 \times 48 =$
A $-20928$ B $-5232$ C $-21028$ D $-20828$

Answer and solution

Answer: (A) $-20928$

Sign: $- \times + = -$

$436 \times 8 = 3488$ , $436 \times 40 = 17440$ , $3488 + 17440 = 20928$

So $-436 \times 48 = -20928$
The value of $-83 \times -99$ is
A $8117$ B $8217$ C $8317$ D $1089$

Answer and solution

Answer: (B) $8217$

Sign: $- \times - = +$

$99 \times 3 = 297$ , $99 \times 80 = 7920$ , $297 + 7920 = 8217$

So $-83 \times -99 = 8217$
$\displaystyle \frac{-62586}{6} =$
A $-10441$ B $-1431$ C $-10431$ D $-104310$

Answer and solution

Answer: (C) $-10431$

$\displaystyle \frac{-}{+} = -$

$6 \div 6 = 1$ ; $2 \div 6 = 0$ r $2$ ; $25 \div 6 = 4$ r $1$ ; $18 \div 6 = 3$ ; $6 \div 6 = 1$

So $\displaystyle \frac{-62586}{6} = -10431$
Only one of these is positive. Which one?
A $\displaystyle \frac{750}{-6}$ B $\displaystyle \frac{-99}{9}$ C $\displaystyle \frac{-468}{-9}$ D $\displaystyle \frac{-912}{4}$

Answer and solution

Answer: (C) $\displaystyle \frac{-468}{-9}$

$\displaystyle \frac{-}{-} = +$ while $\displaystyle \frac{+}{-}$ and $\displaystyle \frac{-}{+}$ are $-$ .

$\displaystyle \frac{-468}{-9} = 52$
Which of these equals $45$ ?
A $\displaystyle \frac{-135}{-3}$ B $-14 - 31$ C $\displaystyle \frac{90}{-2}$ D $-9 \times 5$

Answer and solution

Answer: (A) $\displaystyle \frac{-135}{-3}$

$\displaystyle \frac{-135}{-3}$ : $\displaystyle \frac{-}{-} = +$ and $135 \div 3 = 45$

The others are all $-45$ : $- \times +$ , two negatives added, and $\displaystyle \frac{+}{-}$ .
$-48 + 6 =$
A $-42$ B $-52$ C $-288$ D $-54$

Answer and solution

Answer: (A) $-42$

This is addition with different signs, not multiplication.

$-48 + 6 = -(48 - 6) = -42$

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MCQ test, Set 9