TANCET 2025 Solved Papers

Concept:Using the given average, first fix the total sum of the three quotations. Then check whether the statements together fix the exact value of the highest quotation.Explanation:Let the quotations, in increasing order, be $p \le q \le r$.Given average $= \mathrm{Rs.\ }120$; hence $p+q+r = 120 \times 3 = 360$.Statement (1): the lowest quotation is $\mathrm{Rs.\ }90$. So $p = 90$ and $q+r = 270$.Now $r$ is not fixed; for example, $(90,135,135)$ gives the highest quotation as $135$, while $(90,100,170)$ gives the highest quotation as $170$.Therefore statement (1) alone is not sufficient.Statement (2): one quotation is $\mathrm{Rs.\ }125$. Then the other two quotations together sum to $360 - 125 = 235$.The other two could be $117.5$ and $117.5$, giving the highest quotation as $125$.Alternatively, they could be $80$ and $155$, giving the highest quotation as $155$.Thus statement (2) alone is also not sufficient.Combining both statements: the lowest is $90$ and one quotation is $125$.Since $125 > 90$, the third quotation is $360 - 90 - 125 = 145$.So the three quotations are exactly $90$, $125$, and $145$, and the highest quotation is exactly $145$.Now the required comparison can be answered with certainty.Answer:Option (c): BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.