• Is A greater than B? Or is A more than B?
• Are there less students in school A or are there fewer students in school B?

If you are preparing for your GMAT and such questions haunt you, then you have come to the right place!

It is very likely that on the GMAT sentence correction question you might narrow down the contenders for right answer to two options. Both the sentences might appear to be exactly the same except that one uses the word “lesser” while the other uses the word “fewer”. What would the right answer be in such a case? Well, the choice in such sentences would depend on whether the subject is countable or not countable. As a general rule, less/lesser than is used for non-countable amounts whereas fewer than is used for countable amounts. Let us look at specific examples for the two:

• Tom has signed fewer films than Matt (Films are countable – So we use fewer here)
• Tom has lesser talent than Matt (Talent is not countable – So we use lesser here)

As seen above, the choice of word boils down to the simple fact that the amount being measured is countable or not. For instance, one might witness “less rain” but at the same time might witness “fewer rain drops”. Since rain is not countable (we don’t have 1 rain, 2 rain etc), “less rain” is correct. On the other hand, since drops of rain can be numbered (1 raindrop, 2 raindrops, or 100000 raindrops), we use “fewer than”.

Now that we know about the words that are used to describe the “smaller” amounts, what about the words used to describe “more”? Whether the amount is countable or not countable, “more” is to be used.

So A can have more rainfall (not countable) than B, and also A can have more rain drops (countable) than B.

The comparative word that we haven’t discussed yet is “greater than”. So when do we use greater than? “Greater than” is to be used when a comparison is done between the level/degree/number of something. So we can say:

• The sportsmanship of X is a greater than that of Y.

Here the comparison is between the degree/level of sportsmanship of X &Y. So, we use greater here.

A business conference in Boston was attended by male and female delegates from US and Canada. The conference was attended by 100 female delegates; 60 male delegates from Canada; and 150 US delegates.  If the total number of delegates from the two countries at the conference is 300, what is the sum total of male US delegates and female Canadian delegates?

(A)   90

(B)   140

(C)   200

(D)   230

(E)    250

The given information can be arranged in a double-set matrix form as below:

We are asked to find the sum total of male US delegates and female Canadian delegates. Let us first assign variables to the unknowns:

So, we need to find (U_M+C_F)

From the above table, we can see that,

U_M + 60 + 100 = 300

U_M = 300 -160

U_M = 140

Since,

U_M + U_F = 150

U_F = 150 – U_M

U_F = 150 – 140

U_F = 10

Also,

U_F + C_F = 100

C_F = 100 – U_F

C_F = 100 – 10

C_F = 90

These values may now be entered into the double-set matrix:

So, U_M+C_F = 140 + 90 = 230. Option D is correct.

Now that we are familiar with the concept, let us get to the challenge question of the week:

A business conference in Boston was attended by male and female delegates from US and Canada. The conference was attended by 100 female delegates; 60 male delegates from Canada; and 150 US delegates.  If the total number of delegates from the two countries at the conference is 300, what is the sum total of male US delegates and female Canadian delegates?

(A)   90

(B)   140

(C)   200

(D)   230

(E)    250

The solution to the problem with detailed explanation will be posted tomorrow.  Happy Solving!

Update: The Solution to this problem is posted in this detailed post here. Try attempting the question and then jump to the solution.

Tim and Tom always work at their respective constant rates. If it takes Tim and Tom, working together, 6 hours to paint a house of a certain size, how many more hours does it take Tim, working alone, to paint the house than it takes Tom, working alone?

(1) Tom, working alone, paints a house of this size in twice the time than Tim, working alone, does.

(2) Tim and Tom, working together, paint a house of this size in three-fourths the time that Tim, working alone, does.

 

(A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

(B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

(C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

(D) EACH statement ALONE is sufficient.

(E) Statements (1) and (2) TOGETHER are NOT sufficient.

 

Using the combined rate formula, we can express the time it would take Tim and Tom, individually, to paint the house as follows:

(1/Tim) + (1/Tom) = 1/6

From the question, we have one two-variable equation.

Statement (1) is sufficient: it gives us another two-variable equation. If Tom takes twice the time,

Tom = 2 x Tim, which we could combine with the given equation to solve for Tim, Tom, and their difference. (However, solving the equations to find the individual rates and the difference is not important. It suffices to know that statement (1) is sufficient to solve for Tim, Tom, and their difference.)

Since statement (1) is sufficient, we can rule out options B, C, and E. The only possibilities that now remain are A or D.

Statement (2) is sufficient: it gives us yet another equation. If it takes 6 hours for the two to paint the house together and that is 3/4^th the time it would take Tim alone,

(3/4)Tim = 6, or Tim = 8. Plug that in to the initial equation, and you can solve for Tom, then find the difference.

Since both (1) and (2) are individually sufficient, the right answer is choice (D).

(1/x) + (1/y) = (1/z)

Attempt the GMAT DS question and type your answer in the comments below. The answer with a detailed explanation will be posted tomorrow.

Tim and Tom always work at their respective constant rates. If it takes Tim and Tom, working together, 6 hours to paint a house of a certain size, how many more hours does it take Tim, working alone, to paint the house than it takes Tom, working alone?

 

(1) Tom, working alone, paints a house of this size in twice the time than Tim, working alone, does.

(2) Tim and Tom, working together, paint a house of this size in three-fourths the time that Tim, working alone, does.

 

(A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

(B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

(C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

(D) EACH statement ALONE is sufficient.

(E) Statements (1) and (2) TOGETHER are NOT sufficient.

UPDATE: The solution to this problem is posted on this page. If you have solved this problem, head over to the solution and check whether you were correct.

Let me now discuss the simple “rules” to do well on the GMAT, the rules that helped me score 720 on the GMAT:

Rule # 1 – Enjoy:

First and foremost, don’t get all tensed about the GMAT exam. From my personal experience, I can assure you that the GMAT is NOT a Pandora’s Box! You will end up doing better if you enjoy the entire exercise and think of it as a fun way to improve your grammar and analytical skills.

Rule # 2 – Plan:

Is one month sufficient to prepare for GMAT? The answer depends on whether you have a study plan or not. One month is ample time to prepare if you have a good study plan and, more importantly, if you stick to the plan. Set aside around 3-4 hours (at least) per day for your preparation, and spend more time on your preparation over the weekend. Divide your time wisely, spending more time on your weaker areas. If a certain section of the GMAT appears tougher to you, spend more time on it. Practice does make perfect (or thereabouts!)

Rule # 3 – Right Study Material:

All I needed for my preparation was the Official Guide. Since the OG is released by the official test makers and consists of old GMAT questions, there is no other more reliable source. Also, I prepared with an older version of OG and did not run helter-skelter to get my hands on the latest version – It is more important to have your concepts right, than to answer the latest questions! Of course, as the GMAT now includes the IR section as well, it might be a good idea to get the version that includes IR. If you have the time, or feel the need for it, additional study material might be a good idea. Taking diagnostic tests is extremely important as well. Diagnostic tests give you a feel of the actual exam and help you understand where you stand with your preparation and what areas need more focus.

Rule # 4 – Take Notes:

Note down whatever you think is important and handy information. For instance, while solving a quant question, if you come to know that “if two similar figures have lengths in the ratio A: B, then their areas will be in the ratio A²:B².” – Note it down! It comes in handy to revise such tidbits a few days before your actual GMAT exam.

Rule # 5 – Time! Time! Time!:

Most of us might do well on the GMAT if we could take our own time to solve the questions. Unfortunately, since GMAT is a timed test, we need to incorporate the time factor into our preparation as well.  It is a good idea to prepare by answering a set of questions within a specific time frame to help you to adapt to the GMAT exam. While answering from the OG, you can set aside 30 minutes for a set of 15 questions to begin with. As you get used to answering the questions within this time frame, try to answer the next set within relatively lesser time. This way you will improve your speed on the GMAT.

This sums up the simple rules I set for myself that helped me do well on the GMAT. Good luck to all of you with your GMAT preparation!

Quite a few quant questions on the GMAT and GRE deal with integers and a lot many of those are about consecutive integers. So it would be a good idea to know a little bit more about consecutive integers.

As an extension to consecutive integers, it is a good idea to know about evenly spaced integers as well. Evenly spaced integers are integers that are a fixed distance from the preceding and succeeding numbers in the set. The following are examples of evenly spaced integers:

• 1,4,7,10,13 (Difference between successive numbers in the set – 3)
• 5,10,15,20 (Difference between successive numbers in the set – 5)

All consecutive integers (21, 22, 23, 24), consecutive even integers (4, 6, 8, 10) and consecutive odd integers (11, 13, 15, 17) are evenly spaced integers. Just remember the following 7 properties that usually come in very handy in Data Sufficiency questions:

1. Mean is equal to the median. For the set {2,4,6,8,10}, the mean and median are both 6.
2. Mean and median are both equal to the average of the first and the last term in the set. For the set {1, 4, 7, 10, 13}, the mean and the median are (1+13)/2 = 7.
3. The sum of all the members of an evenly spaced set is the product of its mean and the number of terms in the set. For the set {1,4,7,10,13}, the sum of all the terms is 7 (mean) * 5 (no. of terms) = 35 (1+4+7+10+13=35)
4. Sum of consecutive integers with odd no. of terms is always a multiple of the number of terms.
   • 1+2+3=6 (a multiple of 3 i.e. the number of terms)
   • 7+8+9+10+11=45 (a multiple of 5 i.e. the number of terms)
5. Sum of consecutive integers with even no. of terms is nevera multiple of the number of terms.
   • 1+2+3+4=10 (is not a multiple of 4 i.e. the number of terms)
   • 7+8+9+10+11+12=57 (is not a multiple of 6 i.e. the number of terms)

On some of my recent trips to Europe, if I went to France, then I went to Italy. If I went to England then I went to Germany. If I went to Italy, then I went to England.
If all of the statements above are true, which of the following must also be true?

(A) If I went to Germany, then I went to France.
(B) If I did not go to Italy, then I did not go to England.
(C) If I did not go to Germany, then I did not go to France.
(D) If I went to Germany, then I went to Spain.
(E) If I did not go to France, then I did not go to Germany.

The solution to the above problem is C.

Let us rearrange the if-then statements to give it a more smooth flow:

• If I went to France, then I went to Italy. (A→B)
• If I went to Italy, then I went to England. (B→C)
• If I went to England then I went to Germany. (C→D)

The above relationship can be represented as A→B→C→D

Option A: If I went to Germany, then I went to France. (D→A)

This may not be true. From the concept, we know that when P→Q then Q may happen even if P does not happen. Similarly, if D happens, it does not mean that A must have happened.

Option B: If I did not go to Italy, then I did not go to England.  (Neg(B)→Neg(C))

This may not be true. From the concept, we know that when P→Q then Neg(P) may not necessarily mean Neg(Q). Similarly, if B did not happen, it does not mean that C did not happen.

Option C: If I did not go to Germany, then I did not go to France.  (Neg(D)→Neg(A))

This is the correct answer. From the concept, we know that when P→Q then Neg(Q) means Neg(P) is true. Similarly, if D did not happen, it means that C did not happen. If C did not happen, it means that B did not happen. If B did not happen, it means that A did not happen. So we can conclude that if D did not happen, then certainly A did not happen.

Option D: If I went to Germany, then I went to Spain. (D→E)

This is out of context since Spain is not discussed in the given question.

Option E: If I did not go to France, then I did not go to Germany.  (Neg(A)→Neg(D))

This is incorrect. From the concept, we know that when P→Q then Neg(P) does not necessarily mean Neg(Q) is true. Similarly, if A did not happen, it means that B may or may not have happened. If B did not happen, it means that C may or may not have happened. If C did not happen, it means that D may or may not have happened. So we cannot conclude whether Neg(D) is true or false.

Attempt the GMAT CR question below and type your answer in the comments below. The answer with a detailed explanation will be posted in a day.

On some of my recent trips to Europe, if I went to France, then I went to Italy. If I went to England then I went to Germany. If I went to Italy, then I went to England.

If all of the statements above are true, which of the following must also be true?

(A) If I went to Germany, then I went to France.
(B) If I did not go to Italy, then I did not go to England.
(C) If I did not go to Germany, then I did not go to France.
(D) If I went to Germany, then I went to Spain.
(E) If I did not go to France, then I did not go to Germany.

• Can you tell me whether “whether” or “if” is grammatically correct?
• If I use the word “whether” instead of “if”, will it make more sense?

The above two questions are enough to explain the concept of “Whether Vs If” in a nutshell. In informal writing style, the words “whether” and “if” are sometimes interchangeable. However, the GMAT has clearly defined roles for the words “whether” and “if” and the two cannot be used interchangeably. Let us look at two sentences where the two words are actually interchanged:

• I don’t know whether Tom likes apples or oranges.

-          I do not know what does Tom prefer – apples or oranges. The choice is between the two fruits.

• I don’t know if Tom likes apples or oranges.

-          I do not know whether Tom likes any fruits at all. The choice is NOT between apples and oranges alone.

However, since the two words are not interchangeable on the GMAT, let us look at the role the two words play:

Whether: “Whether” is used to describe a choice. Whenever a choice is presented in a sentence the word “whether” is to be used.

• I do not know whether this post is useful to you.

This post may be useful to you or it may not be. Since there is a choice, “whether” is used instead of “if”.

So we know, “whether” is to be used whenever there is a choice to be made. But what about “whether or not”? “Whether or not” is not grammatically wrong. Even GMAT allows the use of “whether or not”. However, “Whether” is preferred over “whether or not” since the “or not” is redundant. Since, the idea is to select the BEST of the available answer choices, an answer choice with “whether or not” can still be chosen if the other choices have some grammatical flaws.

If: The word “if” describes a conditional statement.

• If you like this post, you can thank me in the comments!

The use of “if” presents a conditional statement above. If you like the post, (then) you can thank me in your memoir!