In this article certain questions have been randomly taken from different topics of the quantitative section of CAT. Each question has been selected keeping in mind certain challenges you need to manage as a test taker. These challenges may range from concept basics to application orientation and test taking strategies.

**Each of the following questions is followed by two statements. MARK (a) if the question can be answered with the help of statement I alone; (b) if the question can be answered with the help of statement II alone; (c) if both, statement I and statement II are needed to answer the question, and (d) if the statement cannot be answered even with the help of both the statements.**

**1. If R is an integer between 1 & 9, P – R = 2370, what is the value of R? **

**P is divisible by 4. ****P is divisible by 9.**

__Topic__ : Numbers

__Approach__ :From the question we can figure out that P lies between 2371 and 2379, both included. Using statement I: P = 2372 or 2376 Using statement II: P = 2376 Hence, Statement II alone is sufficient to get a unique value of R.

__Answer__: b

__Challenge__ :Understanding that multiple values do not qualify as an answer in data sufficiency questions; the value has to be unique

**2. A man distributed 43 chocolates to his children. How many of his children are more than five years old? **

**A child older than five years gets 5 chocolates. ****A child 5 years or younger in age gets 6 chocolates.**

__Topic__ :Numeric Logic

__Approach__ : As 43 is neither a multiple of 5 nor 6, either statement alone is not sufficient to answer the question.

Using both statements together: Let the number of children older than 5 years be ‘x’ and that of 5 years or younger be ‘y’. As per the given information, 5x + 6y = 43.

Thus, 5x = 43-6y

For RHS to be a multiple of 5, the only value y can take is 3; for which the corresponding value of x is 5

__Answer__ : c

__Challenge__ :Applying the concept of multiples in word problems

**3. Ramu went by car from Calcutta to Trivandrum via Madras, without any stoppages. The average speeds for the entire journey was 40 kmph. What was the average speed from Madras to Trivandrum? **

**The distance from Madras to Trivandrum is 0.30 times the distance from Calcutta to Madras. ****The average speed from Madras to Trivandrum was twice that of the average speed from Calcutta to Madras.**

__Topic__ : Time-Speed-Distance

__Approach__ :None of the statements alone is sufficient to answer the question.

Using both statements together: Let the distance and average speed between Calcutta and Madras be ‘x’ km and ‘y’ kmph respectively.

Average speed = Total Distance/Total Time = 1.3x /(x/y + 0.3x/2y) = 1.3/(1/y + 0.3/2y)=40

Since y is the only unknown, its value can be determined and hence the average speed between Madras and Trivandrum can be found. Thus we require both statements to answer the question.

__Answer__ : c

__Challenge __:Application of the concept of average speed particularly when the journey is linearly split between two points

**4. x, y, and z are three positive odd integers, Is x + z divisible by 4? **

**y – x = 2. ****z – y = 2.**

__Topic__ : Numbers

__Approach__ :As none of the statement gives information about all three – x, y and z, they alone are not sufficient to answer the question. Using both statements together: x, y and z are three consecutive odd integers. Therefore x + z is not divisible by 4; because x+z= 2x+4= 2(x+2) which is not a multiple of 4 for odd x.

__Answer__ : c

__Challenge__ :Application of the concept of divisibility and integers

**5. The unit price of product P1 is non-increasing and that of product P2 is decreasing. Which product will be costlier 5 years hence? **

**Current unit price of P1 is twice that of P2. ****5 years ago, unit price of P2 was twice that of P1.**

__Topic__: Equations

__Approach__ :Although using both the statements we can find out by how much has the price of P1 and P2 changed over the 5 years, we cannot answer the question that is being asked as there is no mention of the rate of change.

__Answer__ : d

__Challenge__ :Understanding quantitative comparisons under given conditions

**6. X is older than Y, Z is younger than W and V is older than Y. Is Z younger than X? **

**W may not be older than V. ****W is not older than V.**

__Topic__ : Basic Logic

__Approach__ :X > Y, Z < W and V > Y. If we were to look at all of them we can say that, X,V> Y & W > Z. The first statement gives a uncertain situation using “may”, hence we cannot definitely say about the answer. The second statement says, V > W and hence V > Z. This again does not say anything because we do not know whether X>Z or X<Z.

__Answer__ : d

__Challenge__ :Analysing quantitative comparisons under given conditions

**7. How long did Mr. X take to cover 5000 km journey with 10 stopovers? **

**The x**^{th} stopover lasted x^{2} minutes. **The average speed between any two stopovers was 66 kmph.**

__Topic__ : Time-Speed-Distance

__Approach__ :From statement I we can find that the stopping time was (1^{2}+2^{2}+3^{2}+…..10^{2}) minutes But this statement alone is not sufficient to answer the question. From statement II, average speed between stopovers can be determined but we cannot find total time from the source stop to the destination stop. Thus, this statement alone is also not sufficient.

__Answe__r : d

__Challenge__ :Understanding the application of time-speed-distance in case of multiple stoppages