Practice is the Key to Accuracy in CAT
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Practice is the Key to Accuracy in CAT

Published by: Sandeep kr (62)
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In continuation of our CAT series, we again focus on the Quantitative Ability section of the paper. We have listed five problems that make use of an important theorem. Try out the problems to see where you stand in your preparation for the exam, to be held between October 27 and November 24 this year.

1. The ratio of the present ages of A and B is 3: 4. 15 years later, the ratio of their ages will be 16: 33. What is the present age of A? a) 6 b) 9 c) 12 d) 15 e) Data Inconsistent* Solution: This question can fox students initially. It is based on the fundamentals of ratios. One of the rules called componendo states that if the value of a fraction is less than one, which is the case in this question, then its value will increase when a constant is added to both the numerator and the denominator.

Hence, the ratio of the ages 15 years later will be higher than 3: 4. Since 16: 33 is smaller than 3: 4, it is not possible to solve the question due to inconsistent data. Hence, the correct answer is the option ‘ e’. 2. What is the unit digit of the expression 1! + 2! + 3! +…+ 100!? a) 0 b) 2 c) 3* d) 5 e) Cannot be determined Solution: It looks difficult but for any natural number greater than 4, the factorial of the number will have the unit digit as 0. For example, 5! is 1x2x3x4x5 = 120. Hence, the sum of unit digits of the first four, i. e., 1! + 2! + 3! + 4! which translates into 1+ 2+ 6+ 24 = 33 resulting in ‘ 3’ ( option ‘ c’) being the right answer.

3. 10 27 – 1 is divisible by : a) 9* b) 11 c) 99 d) All of a, b & c e) None of a, b or c Solution: This simple question misleads many students since they think 10 27 – 1 will contain twenty six 9s and will therefore be divisible by each option, i. e., 9, 11 and 99. But actually, it contains twenty seven 9s. Thus, it is divisible only by 9.

Therefore, the correct answer is option ‘ a’. 4. An isosceles trapezium is circumscribed about a circle. One of the parallel sides is thrice the other. Find its area in sq. cm. if the perimeter is 8 cm.

a) 2 ã 3* b) 3 ã 3 c) 4 ã 3 d) 6 ã 3 e) 5 ã 3 Solution: This is another classic CAT kind of question that looks difficult! But options help you to find the answer. We know using the concepts of maxima- minima that the trapezium that has the largest area for a given perimeter is a sqaure! Since its perimeter is 8 cm, the area of the square with the perimeter of 8 cm will be 4 sq cm. Any trapezium having a perimeter of 8 cm will therefore will have an area less than 4 sq cm. The correct answer therefore is option ‘ a’, which is less than 4. All others being higher get elimiated.

5. Three clocks A, B and C are set to show correct time at 12 noon.

When A shows 2 pm, B shows 2.08 pm. When B shows 2.40 pm, C shows 2.44 pm. What will A show when C shows 3.25 pm? a) 3.07.30pm b) 3.10pm c) 3.05.30pm d) 3.50pm e) can’t be determined Solution: This is a variation of the classic Time, Speed and Distance question. This clock question can be easily solved by making a small table that uses proportionality: Clock A Clock B Clock C 120 min 128 min 150 min 160 min 164 min 187.5 min 205 min Step 1: Using proportionality to establish the relationship between time shown in clock A v/ s clock C, when clock C shows 2.44 pm ( 164 minutes past 12 noon ), clock A will show 2.30 pm ( 150 min past 12 noon ).

Step 2: Hence, when clock C shows 3.25 pm (205 min past 12 noon), clock A will show 3.07.30 pm. Therefore, the correct answer is option ‘ a’.

Sandeep kr - About the Author:

OnlineDuniya.com is one of the leading website who provides the information about CAT Exam. You can also get the knowledge of CAT Preparations and MBA Entrance Exam.

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