Latest CAT Aptitude Question SOLUTION: A shop stores x kg of rice. The first customer buys half this amount plus half a kg of rice. The second customer buys half the remaining amount plus half a kg of rice. Then the thi

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(#M40011021) CAT Numerical Ability question Keep an EYE

A shop stores x kg of rice. The first customer buys half this amount plus half a kg of rice. The second customer buys half the remaining amount plus half a kg of rice. Then the third customer also buys half the remaining amount plus half a kg of rice. Thereafter, no rice is left in the shop. Which of the following best describes the value of x?
A. 2 ≤ x ≤ 6
B. 5 ≤ x ≤ 8
C.9 ≤ x ≤12
D. 11≤ x ≤ 14

Asked In CAT Priya (11 years ago)

Unsolved Read Solution (4)

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P M Anoop Sabir  (11 years ago)

after 1st customer, x-x/2-1/2=(x-1)/2
after 2nd customer, (x-1)/2-(x-1)/4-1/2=(x-3)/4
after 3rd customer, (x-3)/4-(x-3)/8-1/2=(x-7)/8=0
x=7 Hence option B.

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Priya  (11 years ago)

A. 2 ≤ x ≤ 6 B. 5 ≤ x ≤ 8 C.9 ≤ x ≤ 12 D. 11≤ x ≤ 14
these are the options

Is this solution Helpfull? Yes (2) | No (1)  

shreeprakash  (7 years ago)

Initial quantity of the rice = x
The first customer buys half the total rice and another half kg.
Rice purchased by first customer = x/2 + 1/2 = (x + 1)/2
So, rice left after the first customer = x - (x + 1)/2 = (x - 1)/2
Now the second customer buys half the left rice and another half kg.
Rice purchased by second customer = (x - 1)/4 + 1/2 = (x + 1)/4
So, rice left after the second customer = (x - 1)/2 - (x + 1)/4 = (x - 3)/4
Now the third customer buys half the left rice and another half kg.
Rice purchased by third customer = (x - 3)/8 + 1/2 = (x + 1)/8
So, rice left after the second customer = (x - 3)/4 - (x + 1)/8 = (x - 7)/8
Given that (x - 7)/8 = 0 => x = 7
So option (b) is correct.

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prabhat gupta  (11 years ago)

b option is correct
by hit and trial method
by taking x=6 and 8.
we get -ve value when we put x=6 and we get +ve value when we put x=8.
so the value must lie between 6 and 8.

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