Test Level 1: Data Sufficiency - 1 (September 4) - CAT MCQ

From I alone, we can figure out that A sits second to the right of C and E could be sitting to the immediate left or right of A.
Thus, we cannot determine the position of D. Hence, statement I alone is not sufficient.
From II alone, we only know about B and D. Thus, II alone is not sufficient.
From I and II together, we can figure out the arrangement like this:

Since we still cannot accurately determine the positions of D and B, statements I and II together are not sufficient to answer the question

I alone is not sufficient because we cannot decode the date. We need to know what day the month started on to get the date on final Monday of October.
II alone is not sufficient because it will only tell us about all the dates and days of October, but any of such day could be his birthday.
I and II together are required because from II, we know that on 15^th, it was Sunday and in a week, there are 7 days. So, (15 - 7) = 8^th October was Sunday and (8 - 7) = 1^st October was a Sunday.
So, last day i.e. 31^st October was a Tuesday. From I, we know that his birthday was on last Monday. i.e. 30^th October was his birthday.

From I only, we get that P has more sweets than both R and S, but we can't deduce that P has most number of sweets. Thus, option 1 isn't correct.
From II alone, we cannot find the answer because of inadequate information. Thus, option 2 isn't correct.
From I and II together, we get that P has more sweets than both R and S and only one person has more sweets than P, and that person could be either Q or T. So, no definite answer is possible.
Therefore, both statements together are insufficient.

Using both statements together, we get the following diagram:

Point X is to the northwest of Point D. Position of D will not make difference in the answer.
So, the data in both statements together is necessary to answer the question.

From I: Total score in 4 subjects = (65 × 4) = 260
From II: Total score (Computer + English) = 190
From III: Total score (English + Maths) = 170
Thus, the data is insufficient to find the answer.

A + B + C + D + E = 70
From I, A = 14, B + C + D + E = 56
From II, B = E - 3 and E = D - 7
So, D = E + 7
From III, C = B + 7 and C = E + 5.
So, the age of every friend can be defined in terms of E's age. Hence, we can find the answer using all three statements together.

• Statements I and II show that Deepak is 2 years older than Kapil and Ankit is also older than Kapil.
• Hence, the ages of Deepak and Ankit cannot be compared.
• Statement III does not provide any clue either.
• Hence, option (4) is correct.

I and III alone do not give any information. Also, II shows that he does not play badminton and hockey, but that does not imply that he plays both the remaining sports. So, I or III combined with II is sufficient to answer the question.

Even using all three statements, we cannot find the distance between D and Q.

From I, we can conclude that 29^th, 22^nd, 15^th, 8^th and 1^st May were all Fridays.
Thus, 8^th May, 2015 was the second Friday of the month.
From II, we can conclude that 31^st May, 2015 was a Sunday.
Thus, 8^th May, 2015 was the second Friday of the month.