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examPAL DS Forum Expert David - Ask Me Anything about GMAT DS

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examPAL DS Forum Expert David - Ask Me Anything about GMAT DS  [#permalink]

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New post 03 Oct 2018, 18:20
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Ask me Anything about GMAT Data Sufficiency


Hello GMAT Club users,
My name is David, nice to meet you :)

I am a senior tutor at examPAL and have been in the test-prep business for years.
This thread is the place for you to ask me anything about DS - from 'how should I approach a question' to 'why is this answer correct' to general tips on the topic you find most difficult.

To start off, the two Most Important DS tips:

Tip Number 1 - DS questions are all about logic.
Figure out what sort of information you need to answer the given DS question BEFORE you look at the given statements. If you can do this (and in most questions you can), it will provide you with enormous focus when analyzing the given statements and is very useful for avoiding various 'traps' that the GMAT loves to use.

Tip Number 2 - There are only 2 types of DS questions.
There are only 2 different kinds of DS questions: 'YES/NO' questions and 'what is the value of...' questions. In both cases, you do not need to actually calculate the value of the answer! In YES/NO questions, you need to figure out if the statements allow you to answer 'yes' or 'no' unequivocally. In other words, given a statement, is the answer always 'yes' or always 'no'? If so, Sufficient! In 'what is the value of' questions you need to figure out if there is EXACTLY one possible value which fits the data in the statement. If there is, Sufficient!
In both cases, you should only make calculations if absolutely necessary!

Best of luck to everyone on their GMAT and remember - the GMAT is just a stepping stone! What is it you actually want to achieve?

See you in the DS forums,
David.

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examPAL DS Forum Expert David - Ask Me Anything about GMAT DS  [#permalink]

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New post 05 Oct 2018, 19:18
Hi DavidTutorexamPAL

Thanks for this awesome initiative.

I falter in converting word problems to algebraic equations.
Can you help with any blog/resources to help understand below sample sentences:
a. Roy has 4 more apples than Sam.
b. The interest in bank A is 1.5 greater than in bank B.

I have least accuracy in work and rate DS problems.
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Re: examPAL DS Forum Expert David - Ask Me Anything about GMAT DS  [#permalink]

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New post 05 Oct 2018, 22:55
1
adkikani wrote:
Hi DavidTutorexamPAL

Thanks for this awesome initiative.

I falter in converting word problems to algebraic equations.
Can you help with any blog/resources to help understand below sample sentences:
a. Roy has more apples than Sam.
b. The interest in bank A is 1.5 greater than in bank B.

I have least accuracy in work and rate DS problems.


Hey adkikani, thanks for the question!

There are two main techniques:
1. Breaking a complex sentence into small bits and looking at each bit separately. This is useful especially when you don't really get what the question is asking you. Instead of trying to figure out everything in your head (and getting confused), write each part down as an equation and only then think about your next steps. You'd be surprised at how much this can help to clarify your understanding.
For example, "The train ran at 55 mph during its entire journey except for the first 10 minutes, where it ran at 10 mph" can be broken down into "55 mph during its entire journey" which can immediately be translated into an equation such as "s = 55". After that, you could continue onto "the first 10 minutes, where it ran at 10mph" and translate it into, for example, "s1 = 10". Only then would you put the 2 equations one next to the other and decide what to do with them.

2. writing things in 'half words - half equations' before in equations. For example, "The interest in bank A is 1.5 times greater than bank B" could be transformed to "interest in A > 1.5 times interest in B" which it is then easier to translate into a full inequality of "A > 1.5B". Note that the purpose of writing things down as equations is to make your life easier - if keeping your equations in 'words' makes them easier for you to understand, do so.

There isn't any specific 'translation tip' for Rate and Work but if you have a specific question you'd like to link to, I'd be happy to go over it.
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Re: examPAL DS Forum Expert David - Ask Me Anything about GMAT DS  [#permalink]

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New post 06 Oct 2018, 21:48
Hello David,

Can you Just suggest me upon how to prepare for DS from scratch?And resources which would prove to be helpful. Everything I need to do for acing the DS section.

Posted from my mobile device
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Re: examPAL DS Forum Expert David - Ask Me Anything about GMAT DS  [#permalink]

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New post 06 Oct 2018, 23:29
1
Shrinidhi wrote:
Hello David,

Can you Just suggest me upon how to prepare for DS from scratch?And resources which would prove to be helpful. Everything I need to do for acing the DS section.

Posted from my mobile device


Hello Shrinidhi,

Thanks for the question!

First off, we made a video on exactly that topic, see it here

In words, the first thing you need to do is realize that there is a very large difference between 'regular multiple choice' PS questions and DS questions.
In PS, you are asked a question and need to calculate the answer to the question.
In DS, you only need to figure out if a certain statement gives you enough information so that you could potentially calculate the answer should you really want to.

For example, if a PS question were to ask you "3^10 = ?" you would actually need to calculate 3 to the power of 10 and look for the relevant answer choice.
If a DS question were to ask you "x^10 = ?" then all you would need to do is look for a statement that tells you the value of x (which would then let you calculate x^10, if you really wanted to).
So "x = 3" would be sufficient as would be "2x + 5 = 11" as would be "x^3 = 27". Each of these allows us to calculate the value of x, which then allows us to calculate the value of x^10. Note that we didn't actually have to complete the calculations! All we had to do was realize that the above statements allow us to calculate the answer, should we want to. This focus on 'sufficiency' and not on 'actually calculating' is the most important thing to realize when going into DS. Once you've got this down, your life becomes much easier and your scores much higher.

The answer choices also reflect this 'information-focus':
Select (A) when the first statement on its own gives you enough information, and the second does not
Select (B) when that the second statement on its own is enough, and the first is not
Select (C) when you must combine both statements to have enough information
Select (D) when each of the statements on its own gives enough information
Select (E) when, even when you combine both statements together, you still don't have enough information

Other than that, much of the routine 'learning the material' work is the same. You need to know the concepts behind, for example, number properties, rate and work, powers and roots, linear equations and so on... You need to learn common GMAT traps, such as missing a negative option or forgetting about zero.

In particular, you need to develop cognitive flexibility - the ability to choose the right tool for the right question. Is it better to just count the number of variables and equations and see if you have enough equations to solve (a Logical approach)? Should you maybe try out a few numbers to help make things concrete (an Alternative approach)? Maybe just dive straight into algebra and simplify (a Precise approach)?

Additionally, you need to learn from your mistakes. Did you miss a negative or positive option? Did you get confused with prime factoring? Every mistake you make should be listed in an error log and you should try 'fixing' your mistake before moving on to the next question. You can either build up this error log on your own or you can let someone else do it for you. On our platform, we use an AI to choose, based on each individual student's preferred solution tools and common mistake reasons, the set of questions and solution approaches that are best for them. If you like, give us a go.

If you're having difficulty with a specific question and would like my input on it, please don't hesitate to ask!
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Re: examPAL DS Forum Expert David - Ask Me Anything about GMAT DS  [#permalink]

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New post 08 Dec 2018, 17:59
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(ex 1) A certain store, books are sold. Books are hard cover or soft cover and hard cover books sold $10 each and soft cover books sold $6. Is the number of hard cover books sold greater than that of soft cover books sold?
1) The average price sold of total books is $9
2) The number of hard cover books sold is 100
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Re: examPAL DS Forum Expert David - Ask Me Anything about GMAT DS  [#permalink]

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New post 23 Dec 2018, 11:08
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(integer) If m and n are positive integers, what is the greatest common divisor of m and n?

1)m=n+1
2)m∗n is divisible by 2
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Re: examPAL DS Forum Expert David - Ask Me Anything about GMAT DS  [#permalink]

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New post 23 Dec 2018, 11:23
1
indu1954 wrote:
(ex 1) A certain store, books are sold. Books are hard cover or soft cover and hard cover books sold $10 each and soft cover books sold $6. Is the number of hard cover books sold greater than that of soft cover books sold?
1) The average price sold of total books is $9
2) The number of hard cover books sold is 100


Hey indu1954,

Sorry for only getting to this now, it slipped through my inbox...

Where is this exercise from? At any rate, it is a relatively simple word problem, and the easiest way to approach such problems is usually to first write them out as equations. (Which lets you 'get concrete' instead of getting lost in mental logic)

Specifically, we can label h = 10 and s = 6 for the prices and numh,nums as the respective number of books. Then we need to find out if numh > nums is true.

(1) tells us that (10*numh + 6*nums)/(numh + nums) = 9. We can either do some algebra to get to numh = 3nums and therefore numh > nums or we can we the concept of weighted average - if we had equal number of hard-cover vs. soft-cover books the average would be the exact middle - 8. Since it is 9, we have more of the expensive books, which are hard-cover.
Either way, this is sufficient.

(2) So we know that numh = 100 but have no way to link nums to an exact number.
This is insufficient.
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examPAL DS Forum Expert David - Ask Me Anything about GMAT DS  [#permalink]

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New post 23 Dec 2018, 11:43
indu1954 wrote:
(integer) If m and n are positive integers, what is the greatest common divisor of m and n?

1)m=n+1
2)m∗n is divisible by 2


Hey indu1954,

The moment you see a question which has the word 'divisor' in it, your immediate thought should be "ooh this is about number properties or factorizations!"
In particular, the GCD is the largest integer that divides both m and n, so we'll either factorize both m and n to find the largest common factor (the Precise approach), or look for some number-theoretic rule that allows us to infer what these factors are without calculations (the Logical approach).

(1) This tells us that the GCD must be 1, which is to say the numbers have no common divisors larger than 1. An easy way to see this is to just try a few examples, a more theoretical (Logical) way inolves using rules of divisors:
Let's label the GCD of m and n as x. Since x divides both m and n, it must also divide m - n (do you understand why?). Then we can write m - n = x*(an integer). Then the equation in the stmt simplifes to x*(an integer) = m - n = 1. This implies that x must divide 1. The only such integer is, of course, 1.
Then (1) is sufficient.

(2) The only thing this tells us is that at least one of m,n is even. With no other information, this cannot be sufficient.

(A) is our answer.
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Re: examPAL DS Forum Expert David - Ask Me Anything about GMAT DS  [#permalink]

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New post 04 Jan 2019, 06:48
Hi DavidTutorexamPAL,

Can you provide an alternative explanation to the below DS problem from one of the examPAL quizes?

Q. a and b are integers. [x] is an integer less than or equal to x. Is \([\frac{a}{b}]\)≥ 1?
(1) \(ab = 64\)
(2) \(a = b^2\)

Here is the official explanation:
Since \([\frac{a}{b}]\) is defined as some integer either equal to or less than \(\frac{a}{b}\), no possible value of (a,b) can ever make \([\frac{a}{b}]\) necessarily greater than any integer. This means a definitive answer to the question stem, if there is sufficient information, can only be ‘NO!’ – when \([\frac{a}{b}]\) < 1. This would be the case if b is greater than a. (1) gives us no such information, and (2) gives us the opposite: the greater integer b is, integer a becomes even greater. Thus, combining the two we’ll still get a > b. Therefore, (E) is correct.

And here is my thought on this question:
Combining (1) and (2), we can get b = 4 and a = 16. So, \(\frac{a}{b} = \frac{16}{4} = 4\) and hence \([\frac{a}{b}] = [4] = 4\).
So, the answer to the above DS question should be C.
Kindly let me know where I am wrong.
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examPAL DS Forum Expert David - Ask Me Anything about GMAT DS  [#permalink]

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New post 04 Jan 2019, 07:33
1
tarunanandani wrote:
Hi DavidTutorexamPAL,

Can you provide an alternative explanation to the below DS problem from one of the examPAL quizes?

Q. a and b are integers. [x] is an integer less than or equal to x. Is \([\frac{a}{b}]\)≥ 1?
(1) \(ab = 64\)
(2) \(a = b^2\)

Here is the official explanation:
Since \([\frac{a}{b}]\) is defined as some integer either equal to or less than \(\frac{a}{b}\), no possible value of (a,b) can ever make \([\frac{a}{b}]\) necessarily greater than any integer. This means a definitive answer to the question stem, if there is sufficient information, can only be ‘NO!’ – when \([\frac{a}{b}]\) < 1. This would be the case if b is greater than a. (1) gives us no such information, and (2) gives us the opposite: the greater integer b is, integer a becomes even greater. Thus, combining the two we’ll still get a > b. Therefore, (E) is correct.

And here is my thought on this question:
Combining (1) and (2), we can get b = 4 and a = 16. So, \(\frac{a}{b} = \frac{16}{4} = 4\) and hence \([\frac{a}{b}] = [4] = 4\).
So, the answer to the above DS question should be C.
Kindly let me know where I am wrong.


Hey tarunanandani
This is a confusing question, because it deals with a function. these can be really tricky sometimes...
read the instructions again: [x] is an integer less than or equal to x. This means that if \(\frac{a}{b} = \frac{16}{4} = 4\), then \([\frac{a}{b}]\) equals... something less or equal to 4 - but we don't know what! it could be 3, 1, -100... we don't know! hence, the answer is insufficient.
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Re: examPAL DS Forum Expert David - Ask Me Anything about GMAT DS  [#permalink]

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New post 10 Mar 2019, 10:03
A certain box has only a total of 7 red balls and green balls. If two balls are selected randomly from the box and one ball at a time with replacement, what is the number of red balls?

1) The probability that two balls selected are green balls is (4/7)(4/7)
2) The probability that two balls selected are not green balls is (3/7)(3/7)
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examPAL DS Forum Expert David - Ask Me Anything about GMAT DS  [#permalink]

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New post 15 Mar 2019, 03:09
indu1954 wrote:
A certain box has only a total of 7 red balls and green balls. If two balls are selected randomly from the box and one ball at a time with replacement, what is the number of red balls?

1) The probability that two balls selected are green balls is (4/7)(4/7)
2) The probability that two balls selected are not green balls is (3/7)(3/7)


So first off, the current wording is a bit unclear; a better wording could be: "A box contains exactly 7 balls, all of which are either red or green. If two balls are selected from the box randomly and with replacement, such that one ball is chosen each time, how many red balls are in the box?"

For (1), the only way to get a probability of \((\frac{4}{7})^2\) is if there were 4 green balls (as the equation implies that you have 4 choices for the first, then replace it and have 4 for the second), implying that there were 3 red balls.
Similarly, stmt (2) says there are 3 red balls.

Then (D) is our answer.

Were you interested in this specific question or in more general concepts relating to probability? As the question itself is a bit basic...
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examPAL DS Forum Expert David - Ask Me Anything about GMAT DS   [#permalink] 15 Mar 2019, 03:09
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