Question

Write down a pair of integers whose sum is -7.
[a] -5,-2
[b] 5,2
[c] -6,-1
[d] Both a and c.

Answer 1

Hint: Check each of the options and find out which of the pairs of integers sum up to -7. Hence find the pair of integers whose sum is -7.

Complete step-by-step answer:
Rules to add two integers:
When we add two integers x and y, we have four cases:
Case I: $x\ge 0,y\ge 0$
In this case, we add the absolute values of x and y and the answer is the result with +sign, i.e. result = |x|+|y|
Case II: $x\ge 0,y<0$
In this case, we compare the absolute values of x and y. If x has larger absolute value, then the answer will have + sign. If y has larger absolute value, then the answer has - sign.
The absolute value of the sum is the difference between the absolute values of x and y.
Consider the case we add 10 and -5. In this case, 10 has larger absolute value, so the answer will have a positive sign. Now since the difference in absolute values $=10-5=5$, the answer will be 5.
Case III: $x<0,y\ge 0$
In this case, we compare the absolute values of x and y. If x has larger absolute value, then the answer will have - sign. If y has larger absolute value, then the answer has + sign.
The absolute value of the sum is the difference between the absolute values of x and y.
Consider the case we add -10 and 5. In this case, -10 has a larger absolute value, so the answer will have a negative sign. Now since the difference in absolute values $=-10+5=5$, the answer will be -5.

Case IV: $x<0,y<0$
In this case, we add the absolute values of x and y and the answer is the result with – sign, i.e. result = -(|x|+|y|)

[a] -5 and -2.
This falls in case IV.
So, we add the absolute values
We have $\left| -5 \right|+\left| -2 \right|=-(5+2)=-7$
Hence the result = -7.
Hence the integers in option [a] sum up to -7.
[b] 5 and 2
This falls in Case I.
So, we add the absolute values
We have $\left| 5 \right|+\left| 2 \right|=7$
So the result = 7.
The integers in option [b] do not add up to 7.
[c] -1 and -6
This falls in case IV.
So, we add the absolute values
We have $\left| -1 \right|+\left| -6 \right|=-(1+6)=-7$
Hence the result = -7.
Hence the integers in option [c] sum up to -7.
Hence option [d] is correct.

Note: In these types of questions we need to take care whether we have to add the absolute values or subtract them and what the sign of the result will be.