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Quant/DI – Venn Diagrams

These type of questions can occur in both quant or DI depending on length and difficulty of the questions. 

I have a presentation made about Venn Diagrams, but I am a little under the weather and am unable to record narration right now. 

The slides are pretty self explanatory so I don’t think anyone will have a problem in understanding them. 

Here you have the presentation in .ppt format. It is only 88.5 Kb. 

Venn Diagrams Tutorial 

Here you go a screenshot of the presentation. 

screenshot_venn_diagrams

Hope you like the tutorial! 

Exercise:

The exercise for similar problems such as the ones solved in the presentation are here.

The  file is in .doc format and is of 37 Kb. 

venn-diagrams-Exercise

Hope you like the post! 

Do come back for more!! 😀 

Your Say – Solution to Ruchi’s Problems

Ruchi asked me a doubt in Number Theory :

Hey thnx nicky
cud u pls temme the soln of the foll ques m nt able 2 solve it .

1234^1235^1236^1237 find the unit digit of this expression .

 

Here is the solution to her problem: 

Solution :

Method 1 – 

1234^1235^1236^1237 = (((1234)^1235)^1236)^1237

 

Now let’s consider the inner most terms -> (1234)^1235 

Using our method given in Number Systems Thoery , we get 

1235/4 gives us Rem = 3

So, last digit of (1234)^1235 = last digit of 4^3 which is 4

Now,

last digit of 

(((1234)^1235)^1236)^1237 is the same as last digit of (4^1236)^1237

 

Now, consider 4^1236 . Last digit of this can be obtained again by using the same technique 

remainder of 1236/4 is 0 , so last digit is last digit of 4^4 which is 6.

Now, similarly, we get  

that last digit of (((1234)^1235)^1236)^1237 is the same as last digit of (6^1237)

Again, we get remainder of 1237/6  as 1. 

So, last digit of(((1234)^1235)^1236)^1237 is last digit of 6^1 which is 6 .

The last digit of(((1234)^1235)^1236)^1237 is 6.

Method 2 – 

If we observe the following 

4*4 = 16

4*4*4 = 64

4*4*4*4 = XX6

4*4*4*4*4 = XX4

 

Therefore, we infer that

– 4 to power of even number gives last digit as 6.

– 4 to power of odd number gives last digit as 4.  

 

Now, we can find out last digit of

1234^1235^1236^1237 = 1234^(1235*1236*1237)

if we know whether 1235*1236*1237 is odd or even.   

As we know that odd * even = even , and 1236 is even, we get that 1234 is raised to even power. 

So, last digit of 1234 ^ even is 6 (from the observation above)

Last digit of 1234^1235^1236^1237 is 6. 

 

Thank you for the problem Ruchi – I enjoyed solving it! 

———————————————————————————————

I hope you liked the way I solved Ruchi’s  problem. If you have any easier method to solve it, do let me know. 

Logical Reasoning – Syllogisms

All Cats are Dogs

Some Dogs are Birds

How do you solve these questions in under a minute?

Check out the presentation here 🙂

It is in .ppt format and is 8 MB in size.

logical-deductions-Syllogisms

A sample presentation without narration is here on slideshare.net

I haven’t put it up here, ’cause it seems to be crashing the blog.

Here’s a screenshot of the presentation 🙂

Logical Reasoning - Syllogisms

Can I guess?

This is one question which bothers most CAT aspirants – “Can I guess?”

“If you can eliminate all options except two, guess…” says Gaurav Bhattacharya, a 100 Percentiler in CAT 2007. Well, I have to dis-agree with him here, as guessing is something much more difficult than actually solving the question.

Why do I say this?

Well, the IIM professors who make the CAT, design it so as to eliminate all chances of people making the cut just-by-chance. They are looking for real intellect and not beginner’s luck.

Guessing is something which can be done only if you have had already experienced similar questions many times before and are sure about what the answer could look/be like. For a problem/question which appears completely new to you, it is wise to let it be and use the time to solve another problem which you know how to solve.

What about guessing in verbal section?

Most students believe that the verbal section is pure luck and works on pure guessing. I know many 99+ percentilers who believe that the law of averages will ensure a 50% accuracy if they answer most of the questions. However, this is not true. Though the verbal ability section looks ambiguous and the answers in the key look unlikely at the first glance, a thorough analysis of the answers will prove otherwise. One needn’t be a Charles Dickens to crack the CAT verbal, nor does he need to answer all the 40 questions.

A person answering 20 questions with 5 mistakes would obtain 55 marks (ie., 75% accuracy) which would be a 96+ percentile – enough to fetch him all calls. While a person answering 38 questions with 19 mistakes (50% accuracy) would be getting the same 57 marks. However, answering 20 questions would take much less time and effort compared to answering 38 questions. A person answering 20 questions can even leave out a whole Reading Comprehension passage which he finds difficult or time consuming while a person answering 38 questions would have spent at least 10 – 15 mins on the same passage and also guessing through it to attain such a high attempt rate.

A similar logic can be applied to QA or DI sections.

Solving 12 problems with no mistakes out of 30 in QA/DI would fetch you 48 marks which is 98+%ile while answering 18-20 questions out of 30 with 6-8 mistakes can cost you a call from the top 3 IIMs.

Its not the number of questions you answer, but the number of questions you answer RIGHT.

Remember, you don’t need to top in the CAT – you just need to clear all cut offs and clear the final cut off – for which you don’t need to be a super human.

Solutions: Reading Comprehension-1 (CAT 2008)

Here is the answer key. The solutions have been narrated in the audio. Though it is 10 mins long, it is of very horrible quality :P – this was done to decrease size. So, I presume it should download fine.

Do NOT play the slideshow. Instead, open the presentation and double click on the “speaker” icon to listen to the narration.

The file is in a powerpoint presentation format.

Reading-Comprehension-1-cat-08

Solution with Explanation – Narrative in .pptx format – 5.65 MB

Answer Key:
Q 76. Option 3
Q 77. Option 4
Q 78. Option 2
Q 79. Option 2
Q 80. Option 1

I hope you like my technique and try practicing with it. You can use the other two techniques also, if you find them easier.

Reading Comprehension -1 (CAT 2008)

Read the passage below and try to answer the questions. This is an RC passage from CAT 2008.

You can download the CAT 2008 paper from here. It is by TestFunda.com

The following passage has been obtained from Learnhub.com

Directions for Questions 76 to 80 The passage given below is followed by a set of five questions. Choose the most appropriate answer to each question.

When I was little, children were bought two kinds of ice cream, sold from those white wagons with the canopies made of silvery metal: either the two-cent cone or the four-cent ice cream pie. The two-cent cone was very small, in fact it could fit comfortably into a child’s hand, and it was made by taking the ice cream from its container with a special scoop and piling it on the cone. Granny always suggested I eat only a part of the cone, then throw away the pointed end, because it had been touched by the vendor’s hand (though that was the best part, nice and crunchy, and it was regularly eaten in secret, after a pretense of discarding it).

The four-cent pie was made by a special little machine, also silvery, which pressed two disks of sweet biscuit against a cylindrical section of ice cream. First you had to thrust your tongue into the gap between the biscuits until it touched the central nucleus of ice cream; then, gradually, you ate the whole thing, the biscuit surfaces softening as they became soaked in creamy nectar. Granny had no advice to give here: in theory the pies had been touched only by the machine; in practice, the vendor had held them against his hand while giving them to us, but it was impossible to isolate the contaminated area.

I was fascinated, however, by some of my peers, whose parents bought them not a four-cent pie but two two-cent cones. These privileged children advanced proudly with one cone in their right hand and one in their left; and expertly moving their head from side to side, they licked first one, then the other. This liturgy seemed to me so sumptuously enviable, that many times I asked to be allowed to celebrate it. In vain. My elders were inflexible: a four-cent ice, yes; but two two-cent ones, absolutely no.

As anyone can see, neither mathematics nor economy nor dietetics justified this refusal. Nor did hygiene, assuming that in due course the tips of both cones were discarded. The pathetic, and obviously mendacious, justification was that a boy concerned with turning his eyes from one cone to the other was more inclined to stumble over stones, steps, or cracks in the pavement. I dimly sensed that there was another secret justification, cruelly pedagogical, but I was unable to grasp it.

Today, citizen and victim of a consumer society, a civilization of excess and waste (which the society of the thirties was not), I realize that those dear and now departed elders were right. Two two-cent cones instead of one at four cents did not signify squandering, economically speaking, but symbolically they surely did. It was for this precise reason, that I yearned for them: because two ice creams suggested excess. And this was precisely why they were denied me: because they looked indecent, an insult to poverty, a display of fictitious privilege, a boast of wealth. Only spoiled children ate two cones at once, those children who in fairy tales were rightly punished, as Pinocchio was when he rejected the skin and the stalk. And parents who encouraged this weakness, appropriate to little parvenus, were bringing up their children in the foolish theater of “I’d like to but I can’t.” They were preparing them to turn up at tourist-class cheek-in with a fake Gucci bag bought from a street peddler on the beach at Rimini.

Nowadays the moralist risks seeming at odds with morality, in a world where the consumer civilization now wants even adults to be spoiled, and promises them always something more, from the wristwatch in the box of detergent to the bonus bangle sheathed, with the magazine it accompanies, in a plastic envelope. Like the parents of those ambidextrous gluttons I so envied, the consumer civilization pretends to give more, but actually gives, for four cents, what is worth four cents. You will throw away the old transistor radio to purchase the new one, that boasts an alarm clock as well, but some inexplicable defect in the mechanism will guarantee that the radio lasts only a year. The new cheap car will have leather seats, double side mirrors adjustable from inside, and a paneled dashboard, but it will not last nearly so long as the glorious old Fiat 500, which, even when it broke down, could be started again with a kick.

The morality of the old days made Spartans of us all, while today’s morality wants all of us to be Sybarites.

Q. 76. Which of the following cannot be inferred from the passage?

(1) Today’s society is more extravagant than the society of the 1930s.
(2) The act of eating two ice cream cones in akin to a ceremonial process.
(3) Elders rightly suggested that a boy turning eyes from one cone to the other was more likely to fall.
(4) Despite seeming to promise more, the consumer civilization gives away exactly what the thing is worth.
(5) The consumer civilization attempts to spoil children and adults alike.


Q. 77. In the passage, the phrase “little parvenus” refers to

(1) naughty midgets
(2) old hags
(3) arrogant people
(4) young upstarts
(5) foolish kids


Q. 78. The author pined for two-cent cones instead of one four-cent pie because

(1) it made dietetic sense
(2) it suggested intemperance

(3) it was more fun
(4) it had a visual appeal
(5) he was a glutton


Q. 79. What does the author mean by “now a days the moralist risks seeming at odds with morality”?

(1) The moralist of yesterday have become immoral today
(2) The concept of morality has changed over the years
(3) Consumerism is amoral
(4) The risks associated with immorality have gone up
(5) The purist’s view of morality is fast becoming popular


Q. 80. According to the author, the justification for refusal to let him eat two cones was plausibly

(1) didactic
(2) dietetic
(3) dialectic
(4) diatonic
(5) diastolic