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# CAT 1991 Question – Find the result closest to the product

Q.)X,Y and Z are three positive integers such that X>Y>Z. Which of the following is closest to the product XYZ?
A)(X-1)YZ
B)X(Y-1)Z
C)XY(Z-1)
D)X(Y+1)Z

Solution :

Given Options are :

(X-1)YZ = XYZ – YZ

X(Y-1)Z = XYZ – XZ

XY(Z-1) = XYZ – XY

X(Y+1)Z = XYZ + XZ

From the given options, we need to find out the minimum of YZ , XZ ,XY .

Given X>Y>Z

Y>Z , Multiplying X on both sides , We get XY > XZ —–(I)

X > Y , Multiplying Z on both sides , We get XZ > YZ ——(II)

From (I) and (II) , We get

XY > XZ > YZ.

Hence , least is YZ.

So, the value which is closest to the product XYZ = XYZ – YZ (FROM the given Options)

Hence ,OPTION(A)

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