GMAT data sufficiency strategy - assume,check and adjust

Stumped with data sufficiency...

Data sufficiency is a test of mathematical reasoning.  It tests your ability to evaluate the adequacy of given data in answering a question in the mathematical setting. This involves verifying the sufficiency of data to solve a problem, distinguishing between relevant and irrelevant data, and establishing relationship between variables.

Here’s how the directions for data sufficiency problems appear in the exam

A given question is followed by two statements. You are required to determine whether the statements can be used to answer the question.

Mark (A) if statement I alone is sufficient but statement II alone is not sufficient to answer the question

Mark (B) if statement II alone is sufficient but statement I alone is not sufficient to answer the question

Mark (C) if both statements I and II together are sufficient to answer the question

Mark (D) if each statement alone is sufficient to answer the question

Mark (E) if statement I and II together are not sufficient to answer the question

Let us understand one approach to solve DS questions with lots of variables

Let’s take a question

Is the product abcd = 1?        

Statement 1: ab/cd=1

Statement 2: a,b,c,d are integers

Strategy:

Take a statement. Substitute different sets of numbers and check for consistency. If the results are inconsistent, when different sets of number are substituted, the given statement is insufficient. 

Lets solve this question with this approach

Is the product abcd = 1?        

Statement 1: ab/cd=1

Statement 2: a,b,c,d are integers

Consider statement 1

Substitute numbers which satisfy statement 1

a=2,b=3,c=6 and d=1 satisfy statement 1. But is the product abcd= 1. The answer is “no”

Plug in a different set of numbers to check consistency

a=4,b=3,c=6 and d=2 satisfy statement 1. Is the product abcd= 1. The answer is “no”

But

a=2,b=1/2,c=3 and d=1/3 satisfy statement 1. Is the product abcd= 1. The answer is “Yes”.

As the result is inconsistent, sometimes the answer is “yes” other times it is “no”. The given statement is insufficient.

Similarly analyse statement 2

Plug in numbers which satisfy statement2

a=2,b=3,c=6 and d=1 satisfy statement 1. But is the product abcd= 1. The answer is “no”

a=1,b=1,c=1 and d=1 satisfy statement 1. But is the product abcd= 1. The answer is “yes”

Thus statement 2 is insufficient, since, for certain numbers “yes” is arrived and for others “no” is arrived

Even when both statements are combined, for certain numbers “The product abcd is equal to 1” is arrived and for others “The product abcd is not equal to 1” is arrived

It is necessary to arrive at consistent result before marking an answer.

The answer is E.

Try another question with the same approach

Is (a/b)>(c/d)?

1.a>c

2.b>d

Answer is E.

Understanding GMAT data sufficiency question

The next set of blogs will be focusing on Data sufficiency(DS). Many students feel that they make more errors in DS than problem solving. Let us understand this question type in depth.

Sample question:

What is the value of a?

(1)      3a + 2b = 15

(2)      b = (-3/2) (a – 5)

The Directions:

Each data sufficiency problem consists of a question and two statements, labeled (1) and (2), that give data. You have to decide whether the data given in the statements are sufficient for answering the question.

Use the data given in the questions plus your knowledge of mathematics and everyday fact, you must indicate whether the data given in the statements are sufficient for answering the questions and then indicate one of the following answer choices:

(A) Statement (i) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked;

(B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked;

 (C) BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient;

(D) EACH statement ALONE is sufficient to answer the question asked;

(E) Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed.

NOTE: In data sufficiency problems that ask for the value of a quantity, the data given in the statements are sufficient only when it is possible to determine exactly one numerical value for the quantity.

Numbers: All numbers used are real numbers.

Figures: A figure accompanying a data sufficiency problem will conform to the information given in the question but will not necessarily conform to the additional information given in statements (1) and (2).

Lines shown as straight can be assumed to be straight and lines that appear jagged can also be assumed to be straight. You may assume that the positions of points, angles, regions, and so forth exist in the order shown and that angle measures are greater than zero degrees. All figures lie in a plane unless otherwise indicated.

These questions require knowledge of the following topics: • Arithmetic • Elementary algebra • Commonly known concepts of geometry

DS problem – Approach flow chart

Next post: Strategies to tackle data sufficiency questions

Data sufficiency - factors

Data sufficiency

If N = 3^x x 5^y, where x and y are positive integers, and N has 12 positive factors, what is the value of N?

(1) 9 is NOT a factor of N

(2) 125 is a factor of N

The number of factors  is given by formula (x+1)(y+1) where x,y are the powers of the prime numbers after prime factorization.

12 = (x+1)(y+1)

The product of (6,2) (4,3) give 12.

Hence the pair combinations of x and y can be (5,1)(11,0),(3,2) { x =5 and y=1 or x=1 and y=5)

Hence N = 3^x x 5^y

As per statement 1. If 9 is not a factor of N. It means the values of x and y should be (1,5) 

sufficient.

As per statement 2. if 125 is a factor of N, it means the values of x and y can be any combination.

Hence A

Data sufficiency understanding the directions

Data sufficiency is designed to measure your ability to

• Analyse a quantitative problem
•  Recognize which information is relevant
• Synthesize data
• Determine at which point there is sufficient information to solve a problem.

Data sufficiency questions contains a question statement, followed by two sub statements labeled (1) and (2). Do not waste valuable time  solving a problem.  Only determine the statements sufficient to solve a problem. Follow the flow chart presented below.

The order of preference while answering a question is

1. D
2. A/B
3. C
4. E

Scenario 1:

Check question statement and statement (1) first. If you get an answer, wait

Then

Check question statement and statement (2)alone. If you get an answer now mark D

Scenario 2:

Check question statement and statement (1) first. If you get an answer, wait

Then

Check question statement and statement (2)alone. If you do not get an answer now mark A

Scenario 3:

Check question statement and statement (1) first. If you do not get an answer

Then

Check question statement and statement (2)alone. If you do get an answer now mark B

Scenario 3:

Combine question statement ,statement (1) and statement (2).

 If you get an answer now mark C

Scenario 4:

Combine question statement ,statement (1) and statement (2).

 If you do not get an answer now mark E

10 must NOT DOs for GMAT math - Data sufficiency

10 must NOT DOs for GMAT math
the directions to Data sufficiency qns ( some tips below may require you to revisit these directions)This problem consists of a question and two statements, labeled (1) and (2), in which certain data are given. You have to decide whether the data given in the statements are sufficient for answering the question. Using the data given in the statements plus your knowledge of mathematics and everyday facts (such as the number of days in July or the meaning of counterclockwise), you must indicate whether:

A statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked;
B statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked;
C BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient;
D EACH statement ALONE is sufficient to answer the question asked;
E statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.


Now here are some simple not dos
1.Assume that a given number is positive only. The numbers given can be zero, negative fractions or decimals.
i.e. sample
Main statement- is the modulus of X less than 3?
Sub statement 1- X(X+3) <0 Sub statement 2- X(X-3)>0
X can be zero, negative, fraction or decimal.

2. Assume that in a ‘Is...( refer main st in point 1 above ) question type, no is an invalid answer. ‘yes,’ can be a valid answer; no can be a valid answer. ‘sometimes yes and sometimes no’ are invalid.

3. Ignore minimum factors required( that can be gauged from the main st) to answer the qn, if either of the sub statements do not have the min factors, automatically the ans cannot be A or B.
Main st: Is X grater than Y?
Sub st 1. X is greater than Z
Sub st 2. Y is lower than Z
Here as per directions, the ans cannot be A or B.

4. Conclude based on the outcome, while substituting a number to arrive at the answer. Check the outcome while substituting varied numbers i.e. zero,+ve integer,-ve integer,+ve fraction and –ve fraction

5. Hurriedly Mark either A (or B) as the answer option when statement 1(or 2) yields an answer. Study statement 2(or 1)also . If this also leads to answer mark D, else mark A(or B)

6. Spent time deriving absolute values when approximation is sufficient in arriving at a decision.


7. Arriving at numerical values when the question requires only counting the occurrences.


8. Attempt a complex combinatronics problem by attempting to pick/select many objects at a time. pick/select one object at a time. This doesn’t change the final outcome.

9. Follow faulty logic.
i.e. A sample sum
Main statement- is the modulus of X less than 3?
Sub statement 1- X(X+3) <0 Sub statement 2- X(X-3)>0

Correct logic
Determine the range of numbers which satisfy the sub statements
Check whether these numbers satisfy the main statement.


Wrong logic
Determine the range of numbers which satisfy the main statement
Check whether these numbers satisfy the sub statements.

10. Ignoring additional information required to solve the problem
Sample problem
Main statement- A and B takes x and y days respectively to complete a work. How many days will A and B together take to complete it?
Sub statement 1 x=5
Sub statement 2 B alone takes twice as many days as A alone to complete the work

additional information on the efficiency of each person’s work per day is a factor needed. If A works at 50% efficiency, A will take 10 days to complete the work.

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Essentials for GMAT data sufficiency.. Must read

What is Data Sufficiency?

Data sufficiency is designed to measure your ability to

1. Analyse a quantitative problem
2. Recognize which information is relevant
3. Synthesize data
4. Determine at which point there is sufficient information to solve a problem.

Data sufficiency questions contains a question statement, followed by two sub statements labeled (1) and (2). Do not waste valuable time solving a problem. Only determine the statements sufficient to solve a problem.

Follow the flow chart presented below.

 The order of preference while answering a question is

• D
• A/B
• C
• E

There are 5 possible scenario's while answering questions. They are:

Scenario 1:

Check question statement and statement (1) first. If you get an answer, wait
Then
Check question statement and statement (2)alone. If you get an answer now mark D

Scenario 2:

Check question statement and statement (1) first. If you get an answer, wait
Then
Check question statement and statement (2)alone. If you do not get an answer now mark A

Scenario 3:

Check question statement and statement (1) first. If you do not get an answer
Then
Check question statement and statement (2)alone. If you do get an answer now mark B

Scenario 4:

Combine question statement ,statement (1) and statement (2).
If you get an answer now mark C

Scenario 5:

Combine question statement ,statement (1) and statement (2).
If you do not get an answer now mark E

I hope you get your DS sums right now. Mail me at george@semanticslearning.com for your GMAT doubts...:-)



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