Q #1

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Directions: Read the following information to answer the question.

Rakesh has the habit of always pouring his tea from the cup into the saucer before drinking it. He fills both the cup and the saucer to only 90% of their capacity (subject to the availability of tea). He also does not drink any tea which is below the 15% mark in the saucer. If he has to pour the tea from the cup into the saucer at least three times before emptying the cup (each time drinking from the saucer till it reaches the minimum level), then what is the maximum possible ratio of the volume of the cup to that of the saucer respectively?

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The tea is poured three times from the cup before it is emptied.

If 100 is the capacity of the saucer, ( it is always to be filled only to 90 level).

- the first time, tea poured is 90

- the second time tea poured is 75

- the third time tea poured is 75

- Total tea is 240

This is 90% of the capacity of the cup. So, capacity of the cup = 240/0.9 = 266^2/3

Ratio of the capacities of cup & sauces

= 266^2/3: 100

= 2^2/3 : 1 = ^8/3 : 1 = 8 : 3

Q #2

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Directions: Read the following information to answer the question.

The difference between the simple interest and the compound interest compounded annually at the rate of 12% per annum on Rs 5,000 for two years will be:

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Answer : Rs 72

Q #3

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Directions: Read the following information to answer the question.

A, B and C went to buy ration from a wholesale market. They had a combined sum of Rs 900. A spent 80%, B spent 70% and C spent 75% of their respective amounts. Now the ratio of amounts left with them is 4 : 9 : 10. Find the ratio of amounts they had in the beginning.

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20% of A : 30% of B : 25% of C = 4 : 9 : 10. Solve to get the answer.

Q #4

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Directions: Read the following information to answer the question.

A three digit number is such that the sum of the digit in the hundred’s place and the ten’s place is 1 more than the digit in the unit’s place. It is also given that the digit in the ten’s place exceeds the square of the digit in the hundred’s place by 1, and that the square of the digit in the units place diminished by 7 is the same as the sum of the squares of the other two digits. What is the number?

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Let, hundred’s digit = x,

Ten’s digit = y and units digit = z

x + y = z + 1 -------------------(1)

x2 + 1 = y -----------------------(2)

x2 + y2 = z2 - 7 ----------------(3)

x + x2 + 1= z + 1

⇒ z = x2 + x

⇒ z2 = x4 + 2x3 + x2---------------(4)

Also, x2 + (x2 +1)2 = x4 + 2x3 + x2 –7

⇒ 2 x3 - 2 x2 = 8 x3 - x2 - 4 = 0

⇒ (x-2) (x2 + x + 2) = 0

x = 2, (since x2 + x + 2 = 0 gives imaginary roots)

∴ From (2), y = (2)2 x2

⇒ Z = x + y – 1 = 2 + 5 – 1 = 6

∴The number is 256

Note : The best approach here is clearly back substitution from the given answer choices.

Q #5

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Directions: Read the following information to answer the question.

These questions are based on the data given below:
Two Resistors R1 and R2 are said to be connected in series if they are connected as per the figure given below.
and their combined resistance, R, across the points A and B is given by R = R1 + R2.
They are said to be connected in parallel if they are connected as per the figure given below and their
Combined resistance, R, across the points A and B is given by 1/R = 1/R1 + 1/R2.
What is the resistance across the two points B and C for the following arrangement, if all the resistances shown are 4 unites each?

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