Practice Quiz on Quantitative Ability

Ram, a farmer, managed to grow shaped watermelons inside glass cases of different shapes. The shapes he used were: a perfect cube, hemi-spherical, cuboid, cylindrical along with the normal spherical shaped watermelons. Thickness of the skin was same for all the shapes. Each of the glass cases was so designed that the total volume and the weight of the all the watermelons would be equal irrespective of the shape.
A customer wants to but water-melons for making juice, for which the skin of the watermelon has to be peeled off, and therefore is a waste. Which shape should the customer buy?

Nikhil’s mother asks him to buy 100 pieces of sweets worth Rs.100. The sweet shop has 3 kinds of sweets, Kaju Barfi, Gulab Jamun and Sandesh. Kaju Barfi costs Rs.10 per piece, Gulab Jamun costs Rs.3 per piece and Sandesh costs 50 paise per piece. If Nikhil decides to buy at least one sweet of each type, then how many Gulab Jamuns should he buy?

A city has a park shaped as a right angled triangle. The length of the longest side of this park is 80 m. The Mayor of the city wants to construct three paths from the corner point opposite to the longest side such that these three paths divide the longest side into four equal segments. Determine the sum of the squares of the lengths of the three paths.

A computer program was tested 300 times before its release. The testing was done in three stages of 100 tests each. The software failed 15 times in Stage I, 12 times in Stage II, 8 times in Stage III, 6times in both Stage I and Stage II, 7 times in both Stage II and Stage III, 4 times in both Stage I and Stage III, and 4 times in all the three stages. How many times the software failed in a single stage only?

There are two circles C₁ and C₂ of radii 3 and 8units respectively. The common internal(Transverse) tangent,T, touches the circles at points P₁ and P₂respectively. The line joining the centers of the circles intersects T at X. The distance of X from the center of the smaller circle is 5 units. What is the length of the line segment P₁P₂?

Ram and Shyam form a partnership (with Shyam as working partner) and start a business by investing Rs.4000 and Rs.6000 respectively. The conditions of partnership were as follows:
* In case of profits till Rs.200,00 per annum, profits would be shared in the radio of the invested capital.
* Profits from Rs.200,001 till Rs.400,000 Shyam would take 20% out of the profit, before the division of remaining profits, which will then be based on ratio of invested capital.
* Profits in excess of Rs.400,000, Shyam would take 35% out of the profits beyond Rs.400,000,before the division of remaining profits, which will then be based on ratio of invested capital.
If Shyam’s share in a particular year was Rs.367000, which option indicates the total business profit (in Rs.) for that year?

Amitabh picks a random integer between 1 and 999, doubles it and gives the result to Sashi. Each time Sashi gets a number from Amitabh, he adds 50 to the number, and gives the result back to Amitabh, who doubles the number again. The first person, whose result is more than 1000, loses the game. Let ‘x’ be the smallest initial number that results in a win for Amitabh. The sum of the digits of ‘x’ is:

Consider the formula,
positive integers. If ⍵ is increased and and ρ are kept constant, then S: