Doubt & Answer Explanation

Doubt

If (x – 5)(y 6)(z – 8) = 1331, then the minimum value of x y z is:



1)
40




2)
33




3)
19




4)
45




5)
Not unique








Correct Answer: 1


Your Answer: Not Attempted


Course: CAT Quantitative



Answer Description

The minimum Sum is obtained when (x – 5) = (y 6) = (z – 8)
Hence (x – 5) = (y 6) = (z – 8) = 11
=> x = 16, y = 5, z = 19
Thus (x y z) = 40








Q20)



If x y z = 21, then the maximum value of (x – 6)(y 7) (z – 4) is:



1)
343




2)
216




3)
125




4)
64




5)
None of these








Correct Answer: 2


Your Answer: Not Attempted


Course: CAT Quantitative



Answer Description

(x – 6)(y 7)(z – 4) will be maximum only when
(x – 6) = (y 7) = (z – 4) = k (say) for a given value of (x y z) = 21
=> x = k 6
=> y = k – 7
=> z = k 4
x y z = 21
=>(k 6) (k – 7) (k 4) = 21
=>3k 3 = 21
=>k = 6
 
Therefore, (x – 6).(y 7)(z – 4) = k³ = (6)³ = 216

i didnt understand the answer plz clarifythnx