Here is another Data sufficiency question. The topic is Mensuration.
Question
A right circular cone has height H and radius R. A small cone is cut off at the top by a plane parallel to the base. At what height above the base the section has been made?
A. H = 20 cm
B. Volume of small cone: volume of large cone :: 1:15
Correct answer is Choice C. Both statements are required to answer the question
Explanatory Answer
From statement A, we know that the height of the initial cone is 20cm. However, nothing is said about the small cone. Hence, we cannot answer the question using statement A. So, we can eliminate choices (1) and (4).
We are down to choices (2), (3) or (5).
From Statement B, we know that the ratio of the volume of the small cone to that of the large cone is 1 : 15.
i.e. (1/3)*pi*r^2*h : (1/3)*pi*R^2*H is 1 : 15 (r is the base radius of the smaller cone and h is the height of the smaller cone)
or r^2 * h : R^2 * H is 1 : 15
From this information, we will not be able to find the answer to h. Hence, we can eliminate choice (2).
Combining the information in the two statements:
When a section is made the two cones are similar triangles. so h/H = r/R
R = rH/h
We know H = 20
h = (1/15) ( rH/h) ( rH/h)*H /r*r)
i.e., h^3 = (1/15)H^3. Substituting H = 20, we can get the value for h.
Choice (3) is therefore, the correct answer.
Saturday, March 21, 2009
Thursday, March 12, 2009
Data Sufficiency : Geometry
Data Sufficiency questions appear either in the Quantitative reasoning section or in the Data Interpretation and LR section of the CAT test.
Usually 5 to 10 questions appear in DS depending upon how many total questions are there in the section.
A data sufficiency question comes with the following set of instructions.
Directions to answer the DS question
1. Statement (A) ALONE is sufficient, but statement (B) alone is not sufficient to answer the question asked.
2. Statement (B) ALONE is sufficient, but statement (A) alone is not sufficient to answer the question asked.
3. BOTH statements (A) and (B) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
4. EACH statement ALONE is sufficient to answer the question asked.
5. Statements (A) and (B) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed
Here is a DS question from Geometry.
Question
Does the circle A with radius ‘a’ touch circle B with radius ‘b’ internally?
A. The two circles touch each other at only 1 point
B. The distance between centers of A and B is a-b
Correct Answer
Choice (2). Statement B alone is sufficient while statement A is not sufficient.
Explanatory Answer
Statement A: The two circles touch each other at only 1 point. If two circles touch each other at only one point, they could touch each other either externally or internally. Hence, this statement is not sufficient to answer the question.
Statement B: The distance between the centers of A and B is a-b. If two circles touch each other internally, then the distance between their centers is the difference between their radii.
As statement B clearly states that the distance between the centers is a - b, the two circles touch each other internally.
Choice (2) is the correct answer.
Some basics about Circles that Touch and Intersect
(i) If two circles touch each other externally, then the distance between their centers is a+ b. There will just be one point at which the circumference of the two circles touch each other.
(ii) If two touch each other internally, then the distance between their centers is a - b, where a > b. There will be only one point at which the circumference of the two circles touch each other.
(iii) If two circles intersect, then there will be two points at which the circumference of the two circles meet. We will not be able to determine the distance between their centers using the information about the radii of the two circles.
Geometry, Coordinate geometry and mensuration are favourite areas in which questions in DS typically appear. Practice with adequate number of questions from your CAT Preparation Material to get familiar with these questions.
Usually 5 to 10 questions appear in DS depending upon how many total questions are there in the section.
A data sufficiency question comes with the following set of instructions.
Directions to answer the DS question
1. Statement (A) ALONE is sufficient, but statement (B) alone is not sufficient to answer the question asked.
2. Statement (B) ALONE is sufficient, but statement (A) alone is not sufficient to answer the question asked.
3. BOTH statements (A) and (B) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
4. EACH statement ALONE is sufficient to answer the question asked.
5. Statements (A) and (B) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed
Here is a DS question from Geometry.
Question
Does the circle A with radius ‘a’ touch circle B with radius ‘b’ internally?
A. The two circles touch each other at only 1 point
B. The distance between centers of A and B is a-b
Correct Answer
Choice (2). Statement B alone is sufficient while statement A is not sufficient.
Explanatory Answer
Statement A: The two circles touch each other at only 1 point. If two circles touch each other at only one point, they could touch each other either externally or internally. Hence, this statement is not sufficient to answer the question.
Statement B: The distance between the centers of A and B is a-b. If two circles touch each other internally, then the distance between their centers is the difference between their radii.
As statement B clearly states that the distance between the centers is a - b, the two circles touch each other internally.
Choice (2) is the correct answer.
Some basics about Circles that Touch and Intersect
(i) If two circles touch each other externally, then the distance between their centers is a+ b. There will just be one point at which the circumference of the two circles touch each other.
(ii) If two touch each other internally, then the distance between their centers is a - b, where a > b. There will be only one point at which the circumference of the two circles touch each other.
(iii) If two circles intersect, then there will be two points at which the circumference of the two circles meet. We will not be able to determine the distance between their centers using the information about the radii of the two circles.
Geometry, Coordinate geometry and mensuration are favourite areas in which questions in DS typically appear. Practice with adequate number of questions from your CAT Preparation Material to get familiar with these questions.
Monday, November 08, 2004
Striking a right balance - Accuracy vs Speed in CAT
Hi
The usual dilemma that one faces while preparing for CAT takes the form of a trade off between accuracy and speed. Honestly, one need not trade off one for the other. In fact, to use a combinatorial term, these two are not mutually exclusive events. However, I will not definitely conclude these two events to be independent ones.
Accuracy is important. But you are not launching a space ship. Essentially this means that you should not hesitate to approximate whenever needed and proceed. For instance, if you realize that you have to find the amount of time taken by two pipes A and B to fill a tank. If these two pipes individually take 20 and 30 minutes respectively, do not spend time trying to solve the problem as 1/20 + 1/30 and then find the LCM and then the answer. If a pipe takes 20 minutes to fill a tank, it fills 5% in a minute. Similarly, another pipe takes 30 minutes to fill a tank, it fills 3.33% in a minute. So, together they fill over 8% a minute. This means they will take about 12 minutes to fill the tank. This kind of approximation and switching between % and fractions will help you gain time.
Similarly, one important thing that you need to keep in mind is that as you proceed with each step of solving a question, take a quick glance at the answer choices. This way, in may instances, you will find that you do not have to go to the last step and find the answer. Even if it is only one or two steps saved for each problem, that will give you enough time to crack another 3 or 4 more problems in CAT. That is a huuuuge difference when it comes to getting calls from the IIMs.
Best wishes
K S Baskar
PGDM - IIM Calcutta - Class of 94
Ascent Education - CAT GDPI Training Sessions
The usual dilemma that one faces while preparing for CAT takes the form of a trade off between accuracy and speed. Honestly, one need not trade off one for the other. In fact, to use a combinatorial term, these two are not mutually exclusive events. However, I will not definitely conclude these two events to be independent ones.
Accuracy is important. But you are not launching a space ship. Essentially this means that you should not hesitate to approximate whenever needed and proceed. For instance, if you realize that you have to find the amount of time taken by two pipes A and B to fill a tank. If these two pipes individually take 20 and 30 minutes respectively, do not spend time trying to solve the problem as 1/20 + 1/30 and then find the LCM and then the answer. If a pipe takes 20 minutes to fill a tank, it fills 5% in a minute. Similarly, another pipe takes 30 minutes to fill a tank, it fills 3.33% in a minute. So, together they fill over 8% a minute. This means they will take about 12 minutes to fill the tank. This kind of approximation and switching between % and fractions will help you gain time.
Similarly, one important thing that you need to keep in mind is that as you proceed with each step of solving a question, take a quick glance at the answer choices. This way, in may instances, you will find that you do not have to go to the last step and find the answer. Even if it is only one or two steps saved for each problem, that will give you enough time to crack another 3 or 4 more problems in CAT. That is a huuuuge difference when it comes to getting calls from the IIMs.
Best wishes
K S Baskar
PGDM - IIM Calcutta - Class of 94
Ascent Education - CAT GDPI Training Sessions
Wednesday, September 29, 2004
2 feet above the paper view of each question
Look at each question from a relatively macro perspective. As you read the question, see if the answer choices give you any clue. More often than not, it will not give much of a clue at this stage. It will just let you get an idea as to whether the answer choices are really close or are they spaced apart. For instance, if you find answer choices for a DI question as 34.3, 34.38, 34.42 and 34.55 skip the question. What is the point in wasting time computing to two decimal points accuracy. Anyway, after you become an MBA you will have the best of calculators and Pentium HT machines at your disposal. What the IIMs are probably testing with such questions is to find out if you are smart enough to skip the question.
You have skipped questions where answer choices really close. What next? Proceed to solve the question. In many instances, even though at the first step answers may not give you much of an idea, as you proceed with the second or third step of solving the problem the answer choices will start making lot more sense. Make it a habit to take a quick glance at the answer choices after each step. It is tantamount to taking a glance at the rear view mirror when you drive a car (that is provided you use the rear view mirror for the intended purpose!!). This time around, it will give you more clues that could help you eliminate answer choices that are not plausible. If your elimination leaves you with only one choice, go ahead and tick it and proceed to the next question. Do Not compute till the last step. It might help get a sense of satisfaction to get the answer after solving all the steps. But then, getting peace of mind in one question will surely cost you missing out on three more.
There will be adequate number of questions in quant section where you should be substituting the answer choices and solving them instead of solving up the logical way. This way you will cut down the time you take for that question by over 50%. Saving time on 10 such questions could mean you will be able to attempt 3 or 4 more questions. Well that is essentially the difference between getting four or more GDPI calls from the IIMs and getting no calls.
Best wishes
K S Baskar
Director - Ascent Education
Visit our archive of CAT Math Question a Day
You have skipped questions where answer choices really close. What next? Proceed to solve the question. In many instances, even though at the first step answers may not give you much of an idea, as you proceed with the second or third step of solving the problem the answer choices will start making lot more sense. Make it a habit to take a quick glance at the answer choices after each step. It is tantamount to taking a glance at the rear view mirror when you drive a car (that is provided you use the rear view mirror for the intended purpose!!). This time around, it will give you more clues that could help you eliminate answer choices that are not plausible. If your elimination leaves you with only one choice, go ahead and tick it and proceed to the next question. Do Not compute till the last step. It might help get a sense of satisfaction to get the answer after solving all the steps. But then, getting peace of mind in one question will surely cost you missing out on three more.
There will be adequate number of questions in quant section where you should be substituting the answer choices and solving them instead of solving up the logical way. This way you will cut down the time you take for that question by over 50%. Saving time on 10 such questions could mean you will be able to attempt 3 or 4 more questions. Well that is essentially the difference between getting four or more GDPI calls from the IIMs and getting no calls.
Best wishes
K S Baskar
Director - Ascent Education
Visit our archive of CAT Math Question a Day
Sunday, September 05, 2004
Skipping tough questions is the key to success
… Do not get unduly concerned if you seem to skipping questions. In the first go attempt only those questions that are really really easy (that will take around a minute or less to answer). Though this is generally true across all three sections, it gains greater importance in the quant section. As you go through each question if you encounter a question that you do not know or happens to be difficult, put an X mark next to it, skip it and forget it. If you find a question that you know, but will take 2 or more minutes, put an A next to it, skip it and proceed. Attempt in the 1st round only those that will take about a minute. After exhausting all these easy questions, if you still have time come back for the questions that you have marked an A. This way, your selection of questions follows the rule of attempting the easiest ones first and then the tougher ones. Putting X and A marks next to the question eliminates the necessity to re select questions when you revisit the section.
On an average, students who crack CAT need to get about 50% or lesser of the number of questions in the quant and DI section as their net score. That essentially translates to skipping every other question, provided you can maintain very high levels of accuracy. So, go ahead and skip questions that are difficult. It will be more detrimental to get stuck in a question and spending a lot of time on it than skipping a question that is easy by mistake.
K S Baskar
Director
Ascent Education - Classes for CAT - XAT - GMAT
On an average, students who crack CAT need to get about 50% or lesser of the number of questions in the quant and DI section as their net score. That essentially translates to skipping every other question, provided you can maintain very high levels of accuracy. So, go ahead and skip questions that are difficult. It will be more detrimental to get stuck in a question and spending a lot of time on it than skipping a question that is easy by mistake.
K S Baskar
Director
Ascent Education - Classes for CAT - XAT - GMAT
Wednesday, August 25, 2004
Keep track of your time. Get your 12 X 10 rhythm in place
Having set time limits for each of the sections that appear in CAT, you need to ensure that your progress is keeping pace in the set time limit.
From my experience of following the last few five or six CATs, I believe that attempting 85 to 90 questions in CAT and getting over 65 as net score is a definite recipe to get calls from couple or more of the IIMs.
With 120 minutes at your disposal, the arithmetic essentially translates to about 7 to 8 questions every 10 minutes. Therefore, divide your 2 hours mentally into 12 slots of 10 minutes and at the end of each 10 minutes do a status check. In reality, you should be doing better in the first half of the time allotted to each section in terms of the number of questions attempted (over 10 every 10 minutes) than the second half. The reason is that you are expected to attempt the easier questions that consume less time in the first half than in the second half.
If you find yourself slipping in any one slot, you need to buck up in the next couple of ones to maintain your average.
If you are in the habit of using a stop watch, make sure that you start it as soon as you get the signal from the invigilator to start the test. There have been instances of students getting tensed on account of not starting their stop watches.
Will add more shortly...
K S Baskar
Director
Ascent Education - Let's get cracking with CAT Preparation
From my experience of following the last few five or six CATs, I believe that attempting 85 to 90 questions in CAT and getting over 65 as net score is a definite recipe to get calls from couple or more of the IIMs.
With 120 minutes at your disposal, the arithmetic essentially translates to about 7 to 8 questions every 10 minutes. Therefore, divide your 2 hours mentally into 12 slots of 10 minutes and at the end of each 10 minutes do a status check. In reality, you should be doing better in the first half of the time allotted to each section in terms of the number of questions attempted (over 10 every 10 minutes) than the second half. The reason is that you are expected to attempt the easier questions that consume less time in the first half than in the second half.
If you find yourself slipping in any one slot, you need to buck up in the next couple of ones to maintain your average.
If you are in the habit of using a stop watch, make sure that you start it as soon as you get the signal from the invigilator to start the test. There have been instances of students getting tensed on account of not starting their stop watches.
Will add more shortly...
K S Baskar
Director
Ascent Education - Let's get cracking with CAT Preparation
Sunday, August 22, 2004
Some essentials to do during the last 90 days to CAT
Hi
With just about 90 days left for CAT here are some things any serious cat aspirant should follow religiously.
First things first. You have less than 15 days to send your completed CAT application forms to the IIMs. So do it as soon as possible. Do not wait for the eleventh hour to send your application and pray that the courier delivers it on time. If you still have not got your application, you have about four days left to get it from one of the IIMs. So do it now!
Here are some of the things that worked for me as I prepared for CAT and things have worked for many others to whom I have had the opportunity to assist in their CAT preparation.
1. Have a clear strategy before your Mock CATs - fine tune it - and use it on November 21st.
Most wars are won not on the power of the ammunition and armor a country possesses but on the power of its think tank. The same is true when it comes to CAT. Before you take any CAT comprehensive test put down on paper the strategy that you want to adopt for that test.
Though the last few CATs did not have any section wise time limit, it would be to your advantage to set those limits yourself.
Typically, students spend about 30 minutes in the verbal section, 40 minutes in the DI section and 50 minutes in the Quant section. This split could vary from individual to individual.
Having set this limit, shave off 5 minutes from each of the sections and keep those 5 minute blocks as reserve. After the first 105 minutes of the test, take a quick call on your performance. If you realize that you have done equally well in all three sections, spend the last 15 minutes in the section that is likely to give you the maximum returns. On the contrary, if you realize that you have not done particularly well in a section, spend the last 15 minutes in this section.
This way you never run short of time for any section. Also this strategy helps you to maximize your returns within the given time frame.
Essentially, do not ever start the test without assigning time limits for the different sections of the test.
Will continue with more tips in subsequent blogs....
Best wishes
K S Baskar
PGDM - IIM Calcutta - Class of '94
Director - Ascent Education - Classes for CAT - XAT - GMAT
Blog Search Engine -Search Engine and Directory of blogs. Looking for blogs? Find them on BlogSearchEngine.com
With just about 90 days left for CAT here are some things any serious cat aspirant should follow religiously.
First things first. You have less than 15 days to send your completed CAT application forms to the IIMs. So do it as soon as possible. Do not wait for the eleventh hour to send your application and pray that the courier delivers it on time. If you still have not got your application, you have about four days left to get it from one of the IIMs. So do it now!
Here are some of the things that worked for me as I prepared for CAT and things have worked for many others to whom I have had the opportunity to assist in their CAT preparation.
1. Have a clear strategy before your Mock CATs - fine tune it - and use it on November 21st.
Most wars are won not on the power of the ammunition and armor a country possesses but on the power of its think tank. The same is true when it comes to CAT. Before you take any CAT comprehensive test put down on paper the strategy that you want to adopt for that test.
Though the last few CATs did not have any section wise time limit, it would be to your advantage to set those limits yourself.
Typically, students spend about 30 minutes in the verbal section, 40 minutes in the DI section and 50 minutes in the Quant section. This split could vary from individual to individual.
Having set this limit, shave off 5 minutes from each of the sections and keep those 5 minute blocks as reserve. After the first 105 minutes of the test, take a quick call on your performance. If you realize that you have done equally well in all three sections, spend the last 15 minutes in the section that is likely to give you the maximum returns. On the contrary, if you realize that you have not done particularly well in a section, spend the last 15 minutes in this section.
This way you never run short of time for any section. Also this strategy helps you to maximize your returns within the given time frame.
Essentially, do not ever start the test without assigning time limits for the different sections of the test.
Will continue with more tips in subsequent blogs....
Best wishes
K S Baskar
PGDM - IIM Calcutta - Class of '94
Director - Ascent Education - Classes for CAT - XAT - GMAT
Blog Search Engine -Search Engine and Directory of blogs. Looking for blogs? Find them on BlogSearchEngine.com
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