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Tackle Options in GMAT DS Questions the Oak’s Academy Way

~ by our Quantitative Reasoning Faculty

 

Step 2 of the Approach to DS Questions: Tackle the Options the Oak’s Way

Step 1 of the approach dealt with carefully reading the question statement (see previous blog). Once that is done you have to deal with the options, which are standard in DS questions:

(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 are needed.

To deal with them in the most systematic way possible just follow the sufficiency/insufficiency table below. It offers the best way of thinking through the options

What’s so great about the Oak’s Way?

What it makes the sufficiency/insufficiency table so cool is that once you’ve found the crux of the question, it will help you to zero in on the answer quickly and efficiently. The essence of the approach is to go step-by-step i.e. first, check STATEMENT (1) for sufficiency/insufficiency and then, do the same for STATEMENT (2). The table below gives you the answer you should choose (last column) depending on whether Statements (!) and (2) are sufficient or insufficient (first and second columns)

 

Statement (1)

Statement (2)

Answer

Sufficient

Sufficient

(D) ‘Each statement alone is sufficient to answer the question asked’

Insufficient

(A) ‘Statement (1) alone is sufficient but statement (2) alone is not sufficient to answer the question asked’

Insufficient

Sufficient

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

Insufficient

If both together are SUFFICIENT

(C) ‘Both statements (1) and (2) together are sufficient to answer the question asked, but neither statement alone is sufficient’

If both together are INSUFFICIENT

(E) ‘Statements (1) and (2) together are not sufficient to answer the question asked and additional data are needed’

 

So, how does it work in an actual question? Let’s have a look at the previous question again.

If x and y are distinct positive integers then:

 

 

 

 

 

 

(1) x = 2 (y + 3)

(2) x2 = y2 + 4

 

Working with Statement (1)

Now, we already know that the only information required to reach the final answer is whether x – y > 0.

According to the GMAT approach we first consider statement (1) that is, x = 2(y + 3) alone.

If we simplify it, we get:

x = 2y + 6

x – 2y = 6.

This tells us that x – y has to be positive (given that x and y are positive integers, in x – y, we are subtracting a smaller value from x than in x – 2y).

Thus, statement (1) alone leads us to conclusion that x – y is must be positive, that is, x – y > 0 and hence, it is sufficient to reach the final answer. This means that our answer has to be either (A) ‘Statement (1) alone is sufficient but statement (2) alone is not sufficient to answer the question asked’ or, (D) ‘Each statement alone is sufficient to answer the question asked’.

 

Working with Statement (2)

To choose between them, we consider statement (2) i.e. x2 = y2 + 4 alone.

If we simplify this, we get:

x2 – y2 = 4

(x + y) (x – y) = 4

Of the two factors we’ve on the left hand side of this equation, (x + y) is always going to be positive as it is an addition of two positive integers and if the product (x + y) (x – y) is 4 (i.e. positive) we can easily conclude that

(x – y) has to be positive! And that again serves our purposes! If x – y is positive, the entire expression in the question definitely has to be positive.

Thus, statement (2) alone is also sufficient and hence, the answer is option (D)!

In this way by using the GMAT approach to the options and making some simple observations, an apparently super complex DS question becomes easy to solve.

 

 

Practice Question

Now, try this question.

Given that a, b, c, d, e are positive integers and that ‘b’ is an odd integer, is the product (a+b)(a+c)(a+d)(a+e) an odd integer?

(1) a is an odd integer

(2) c is an even integer

(For solution click here.)

There is one more thing that you need to know in order to make sure that you get DS questions right. So, my next post will give you one final tip that will help you avoid a mistake that many students commonly make since they are still thinking about DS questions the way that they do about other questions. What’s the tip? Watch for my next post and find out.

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University Application Deadlines For Spring 2014 Semester

Deadlines for the Spring SemesterThe application season is on, June is just round the corner …and university deadlines are coming up soon. So, here is our much awaited blog for university application deadlines for spring 2014 covering 107 universities with application deadlines from June to December for the Spring 2014 semester. At the end is a section on universities with rolling deadlines (click here to find out what is meant by rolling deadlines).

Remember that American universities update deadlines on their websites at different times during the academic year so, we will update this blog to keep up with changes on their official websites.

Presenting the first of our deadline alerts.

Important Question: “Do you know which university you should apply to?”

A deadline is of use only if you know what university you should apply to. For those of you who are not too clear, here is how to decide:

1. Talk to seniors and decide which specialization you should apply for (examples: Networking, Data Bases etc. for Computer Engineers; Digital Signal Processing, VLSI etc. for Electronics and Telecommunications Engineers; MEMS, Robotics etc. for Mechanical Engineers)

2. To find out which universities or colleges offer the specialization you want, go to online.dilipoakacademy.com and look up your college or university in the University Information feature. All you have to do is select a university from the list of the top 220 provided (these have been selected by Mr. Dilip Oak) and you will get a list of departments and courses available. Click here to see. Registration is free and is open to all! (For more details on how to select a university see our ‘Selecting the Right American University for Your MS in the US‘ blog)

3. To plan your application process, check the general deadlines given in this blog. This will give you an idea of how much time you have and how to go about applying.

4. For the exact departmental deadline click the URL at the bottom of the University Information page for that university in online.dilipoakacademy.com. This will give you a more precise idea of how to plan your application process (see our Application Timeline for Spring 2014 blog – to be released in December – to see more specifically how you should go about applying)

Good luck and if your university is not in the list provided, keep looking for it. We will be updating this blog.

Related blogs:

Also see:

Deadlines in June

  1. University of Maryland, Baltimore County –1 Jun
  2. Texas Tech University –15 Jun
  3. University of Tennessee, Knoxville –15 Jun

Deadlines in July

  1. Florida Institute of Technology –1 Jul
  2. University of Pittsburgh –1 Jul
  3. Washington State University, Pullman –1 Jul
  4. North Carolina State University –15 Jul
  5. University of Illinois, Chicago –15 Jul
  6. University of Rhode Island, Kingston –15 Jul

Deadlines in August

  1. Kansas State University – 1 Aug
  2. North Dakota State University, Fargo – 1 Aug
  3. University of Michigan, Dearborn –1 Aug
  4. Western Michigan University, Kalamazoo – 1 Aug
  5. Wichita State University –1 Aug
  6. Rensselaer Polytechnic Institute –15 Aug
  7. South Dakota School of Mines & Tech –15 Aug
  8. South Dakota State University, Brookings –15 Aug
  9. University of Kentucky, Lexington –15 Aug
  10. San Francisco State University – 31 Aug

Deadlines in September

  1. East Carolina University – 1 Sept
  2. George Washington University – 1 Sept
  3. Illinois Institute of Technology, Chicago–1 Sept
  4. Indiana University, Bloomington –1 Sept
  5. Lamar University –1 Sept
  6. Mississippi State University – 1 Sept
  7. Oakland University, Rochester – 1 Sept
  8. University of Alaska, Fairbanks –1 Sept
  9. University of Nebraska, Lincoln –1-Sept
  10. University of Oklahoma, Norman – 1-Sept
  11. University of South Carolina, Columbia – 1 Sept
  12. University of Texas, Dallas –1 Sept
  13. University of Texas, San Antonio – 1 Sept
  14. Virginia Polytechnic Institute & State University – 1Sept
  15. California State University, Chico –15 Sept
  16. Northeastern University, Boston –15 Sept
  17. Texas A & M University, Kingsville –15 Sept
  18. Tufts University –15 Sept
  19. University of North Carolina, Greensboro –15 Sept
  20. University of North Texas, Denton – 15 Sept
  21. California State University, Fresno – 30 Sept
  22. California State University, Northridge – 30 Sept

Deadlines in October

  1. California State University, Sacramento – 1 Oct
  2. Case Western Reserve University – 1 Oct
  3. Eastern Michigan University – 1 Oct
  4. Illinois State University, Normal – 1 Oct
  5. Minnesota State University, Mankato – 1 Oct
  6. Northern Illinois University, DeKalb – 1 Oct
  7. Oklahoma State University, Still Water – 1 Oct
  8. Old Dominion University, Norfolk – 1 Oct
  9. Oregon State University, Corvallis – 1 Oct
  10. Pennsylvania State University, University Park – 1 Oct
  11. Southern Illinois University, Edwardsville – 1 Oct
  12. State University of New York, Stony Brook – 1 Oct
  13. Stevens Institute of Technology – 1 Oct
  14. Tennessee Technological University – 1 Oct
  15. University of Arkansas, Little Rock – 1 Oct
  16. University of Colorado, Denver – 1 Oct
  17. University of Detroit, Mercy – 1 Oct
  18. University of Houston, University Park – 1 Oct
  19. University of Idaho, Moscow – 1 Oct
  20. University of Iowa, Iowa City – 1 Oct
  21. University of Louisiana, Lafayette – 1 Oct
  22. University of Massachusetts, Amherst – 1 Oct
  23. University of Nevada, Las Vegas – 1 Oct
  24. University of New Mexico, Albuquerque – 1 Oct
  25. University of North Carolina, Charlotte – 1 Oct
  26. University of Texas, Arlington – 1 Oct
  27. University of Virginia, Charlottesville – 1 Oct
  28. West Virginia University, Morgan Town – 1 Oct
  29. Worcester Polytechnic Institute – 1 Oct
  30. California State University, Long Beach – 15 Oct
  31. California State University, Los Angeles – 15 Oct
  32. Duke University –15 Oct
  33. Marquette University – 15 Oct
  34. Texas State University – 15 Oct
  35. University of Georgia – 15 Oct
  36. University of South Florida, Tampa – 15 Oct
  37. Villanova University – 15 Oct
  38. California State University, Fullerton – 17 Oct

Deadlines in November

  1. Florida State University – 1 Nov
  2. Idaho State University – 1 Nov
  3. Monmouth University – 1 Nov
  4. University of Louisville, Louisville – 1 Nov
  5. University of Miami, Coral Gables – 1 Nov
  6. University of Utah, Salt Lake City –1 Nov
  7. University of Wyoming, Laramie –1 Nov
  8. Vanderbilt University – 1 Nov
  9. Arkansas State University – 14 Nov
  10. City University of New York, City College –15 Nov
  11. Missouri University of Science & Technology, Rolla –15 Nov
  12. Montana State University, Bozeman –15 Nov
  13. New Jersey Institute of Technology – 15-Nov
  14. University of Massachusetts, Dartmouth – 15 Nov
  15. Marist College, Poughkeepsie – 30 Nov
  16. Southern Methodist University – 30 Nov

Deadlines in December

  1. Lehigh University – 1 Dec
  2. Louisiana Tech University, Ruston – 1 Dec
  3. New York Institute of Technology – 1 Dec
  4. Polytechnic Institute of New York University, Brooklyn – 1 Dec
  5. University of Houston, Clear Lake – 1 Dec
  6. University of South Alabama, Mobile – 1 Dec
  7. University of Southern California–1 Dec

Deadlines in January

  1. Louisiana State University, Baton Rogue – 1 Jan
  2. Wayne State University – 1 Jan
  3. New Mexico Institute of Mining and Technology – 2 Jan
  4. Santa Clara University – 10 Jan
  5. New Mexico State University, Las Cruces – 27 Jan

 

 

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Solutions to GMAT DS Questions

Solution to Question in ‘Tackle Options in GMAT DS Questions the Oak’s Academy Way’ Blog Post

Question:

Given that a, b, c, d, e are positive integers and that ‘b’ is an odd integer, is the product (a+b)(a+c)(a+d)(a+e) an odd integer?

(1) a is an odd integer

(2) c is an even integer

 

 

 

Answer: (D)

 

Solution:

In order to solve this question, we first need to review a few basic addition and multiplication rules:

 

Addition Rules

Multiplication Rules

When Added

Sum

When Multiplied

Product

1. odd + odd =

even

4. odd × odd =

odd

2. odd + even =

odd

5. odd × even =

even

3. even + even =

even

6. even × even =

even

 

Working with Statement (1)

Now according to the method we first take statement (1).

Statement (1) says, ‘a’ is odd and we already know that b is odd (the default information given in the question statement). Since odd + odd = even, the first bracket has to be even. Thus, the first bracket in the multiplication becomes even, and as soon as one number in a multiplication sum becomes even, the product HAS TO BE even (rules 5 and 6)!

Hence, statement (1) is sufficient to solve the question, so the answer has to be either (A) ‘Statement (1) alone is sufficient but statement (2) alone is not sufficient to answer the question asked’ or (D) ‘Each statement alone is sufficient to answer the question asked’’.

 

Working with Statement (2)

In order to decide whether the answer is (A) or (D), we go to the next step in the method: working with statement (2).

Statement (2) tells us that ‘c’ is even. We already know that ‘b is odd’ (the default information given in the question statement). But we have no information about whether ‘a’ is odd or even, so we have to consider both cases.

  • Now, if ‘a’ is odd, the first bracket becomes even (since ‘b’ is odd, and odd + odd is even) and thus, the answer will also be EVEN.
  • If ‘a’ is even, the first bracket becomes odd (since odd + even = odd). HOWEVER, there is one more thing we must note. Since ‘a’ and ‘c’ are even, the second bracket is even. Now, if even one number is even, the entire product has to be even (rule).

Thus, though information given in statement (2) apparently looks ambiguous and irrelevant, it is actually sufficient to reach a final answer!

Therefore, the answer is option (D)!

 

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A Few Great Tips on How to Tackle the GMAT DS Questions

 by our Quantitative Reasoning Faculty

In last time’s blog we looked at why DS is so important in GMAT. In this one we’ll take a look at the 3 key things that you need to do in order to tackle this unfamiliar question type. There are:

 

1. Learn the Options

The first step in learning DS is to get absolutely familiar with the options. Fortunately, in DS, this is easy because the five options are always as follows:

(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 are needed.

 

2. Remember the Aim

Remember, in DS our aim is NOT TO FIND THE FINAL ANSWER to the question but  just to verify whether the INFORMATION GIVEN IN THE TWO STATEMENTS IS SUFFICIENT TO REACH TO THE FINAL ANSWER!

So while solving the question if, at any intermediate step, you realize that you can reach the final answer then QUIT and mark the option accordingly.

 

3. Understand the Approach

Now let’s have a look at how you should approach DS questions.

Step 1: Carefully Read the Question Statement and Find the Crux of the Question

After closely examining the question statement and before you read the information given in statements (1) and (2), ‘identify the crux of the question’. What I mean by ‘the crux of the question’ is the piece of information that is the key to the solution. Sometimes you have to think a little bit before you get it. But once you have it, it will lead you straight to the answer. For example, have a look at this question statement:

 

If x and y are distinct positive integers then:

 

 

 

 

 

(1) x = 2 (y + 3)

(2) x2 = y2 + 4

 

Now, if you have lost touch with maths, just the sight of that forest of terms is enough to want to make you give up. But again, remember that we are not at all interested in solving this inequality. We just need find out whether the expression on the left hand side is positive or not (that’s what is implied by >0) – and this is a much simpler matter! Further, in this mass of algebraic symbols is a key that reveals itself when you examine about the expression and think about it a little.

In order to get this key, the first thing to do is to carefully observe the question statement. First and foremost, it says, that x and y are distinct positive integers. This is a very important piece of information – and you’ll understand why in a moment. Secondly, if you observe the numerator of the expression on the left, it consists of additions throughout. Given both these pieces of information, the numerator has to be positive in nature: it is the sum of distinct positive integers (which is why the information about x and y was important). By the same logic, even the second bracket in the denominator has to be positive. The only unknown factor, therefore, is the first bracket in the denominator, i.e., (x – y) and this is what holds the key to the entire problem.

The entire expression will be positive if and only if (x – y) > 0, in short, if x > y. On the other hand, if x < y, the whole expression will be negative. So, the whole gigantic problem is reduced to an extremely simple question: is x > y? Once we have arrived at this conclusion, cracking the rest of the problem is really easy: any information about the relative magnitudes of x and y will be sufficient to arrive at the answer! Thus, in this case, the crux of the question (the key to the solution) is realizing that all we need to find out in order to answer this question is whether statements (1) and (2) allow us to decide whether x is bigger than y or vice versa.

Once you have reached this stage you are can confidently take on the options of this seemingly insoluble problem. The discussion above takes care of Step 1 of the approach i.e. carefully reading the question statement and finding the crux of the question. In the next post we’ll look at Step 2 of the approach: tackling the options in DS questions – and we’ll be giving you tips that will reduce the complexities to a few simple steps! Watch for the tips in our third DS blog post next week.

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Should I Apply for the Spring Semester (January)?

Many students are interested in joining American universities in January, that is, in the spring semester. But, there is a common misunderstanding that many universities do not accept students in the spring semester and that funding opportunities are also fewer. This, however, is not true. Almost 95% of American universities admit students for the spring semester.

Opportunities for financial assistance in spring are also as good as in fall. Of course, in some universities, a few courses are offered only in the fall semester, so students who join in spring cannot take them. However, with regard to financial aid, most universities offer Research and Teaching Assistantships, tuition waivers etc. only to students who have completed one semester, with a very good GPA (Grade Point Average). Hence, whether you join in the fall or spring semester does not really make a difference.

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