IBPS PO Mains 30 Nov 2024 Shift 2 Paper

Concept:Data sufficiency on cuboid dimensions using given equations.Explanation:Let length, breadth and height be $l$, $b$ and $h$ cm respectively.Statement I gives: $b \times h = 150$.Statement II gives: $\sqrt{l^{2}+b^{2}+h^{2}}=\sqrt{529}$, so $l^{2}+b^{2}+h^{2}=529$.Statement III: Original TSA is $2(lb+bh+lh)$; new length is $1.2l$, so new TSA is $2(1.2lb+bh+1.2lh)$.Increase in TSA is $2(0.2lb+0.2lh)=0.4l(b+h)=200$.Thus $l(b+h)=500$.Now we have three equations: $bh=150$, $l^{2}+b^{2}+h^{2}=529$, and $l(b+h)=500$.Let $S=b+h$. Then $b^{2}+h^{2}=S^{2}-300$ and $l=\frac{500}{S}$.Substitute into statement II: $\left(\frac{500}{S}\right)^{2}+S^{2}-300=529$.This gives $S^{4}-829S^{2}+250000=0$, whose discriminant is negative.So no real value of $S$ exists; the three statements are inconsistent and do not give a unique breadth.Answer:All I, II, and III together are not sufficient to answer the question.Option D.