John spent less than Rs. 75 to buy one kilogram each of potato, onion,

Hi Nailin16,

While solving word problems, the best approach is to introduce variables and translate the question and statements into equations.

The question here tells us that John spent less than Rs. 75 to buy one kilogram each of potato, onion, and gourd. Let the price of potatoes be 'p', the price of onions be 'o' and the price of gourd be 'g'.

So the constraint provided is 1p + 1o + 1g < 75 .

We need to find out which one of the three vegetables p, o and g is the costliest.

Statement 1 : 2 kgs potato and 1 kg gourd cost less than 1 kg potato and 2 kgs gourd.

2p + 1g < 1p + 2g ------> p < g.

Here we just know that the price of potatoes is less than the price of gourd. We do not have any information about the price of onions. Insufficient.

Statement 2 : 1 kg potato and 2 kgs onion together cost the same as 1 kg onion and 2 kgs gourd

1p + 2o = 1o + 2g -----> 1p + 1o = 2g. Substituting this in the constraint 1p + 1o + 1g < 75 we get 2g + 1g < 75 ----> g < 25.

If g < 25 then p + o > 50 and p + o + g < 75. Here we can have p = 26 , o = 25 and g = 23 which makes the potatoes the costliest or we can have p = 25. o = 26 and g = 23 which makes the onions the costliest. Since we do not get a definite answer. Insufficient.

Combining 1 and 2 :

From Statement 1 we have p < g and from statement 2 we have g < 25, since p + o + g < 75 the price of onions will always be greater than 25. Sufficient.

OA : C

CrackVerbal Academics Team