Are negative integers s and t both less than t? 1) s < r+t 2)[m][fract

Solution

Given:
• Both s and t are negative integers

To find:
• Whether the value of s and t less than r

Analysing Statement 1
• As per the information given in Statement 1, s < r + t

o Or, r > s – t

• As it is given that both s and t are negative integers, if we assume that s is less than t, we can have the following scenario possible for r:



Depending on the values of s and t, r can belong to any of the regions indicated.
For example, if s = -7 and t = -1, r > (-7) – (-1) or r > -6
Now, r > -6 means r belong to any of the 3 regions indicated above (red, blue, green)

Hence, statement 1 is not sufficient to answer

Analysing Statement 2
• As per the information given in Statement 2, \(\frac{s}{r}\) < t
• We know that t is negative. Hence \(\frac{s}{r}\) should also be negative.
• We know that s is already negative. Thus, to ensure that \(\frac{s}{r}\) is negative. r MUST be positive.

Hence, from the given statement \(\frac{s}{r}\) < t, we can say r > 0 and \(\frac{s}{t}\) > 0

Hence, statement 2 is sufficient to answer

Hence, the correct answer is option B.

Answer: B