Last visit was: 17 Jul 2025, 06:06 It is currently 17 Jul 2025, 06:06
Close
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Close
Request Expert Reply
Confirm Cancel
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 17 Jul 2025
Posts: 102,601
Own Kudos:
Given Kudos: 98,220
Products:
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 102,601
Kudos: 742,144
Kudos
Add Kudos
Bookmarks
Bookmark this Post
avatar
damamikus
Joined: 10 Jan 2014
Last visit: 12 Oct 2017
Posts: 16
Own Kudos:
Given Kudos: 6
Posts: 16
Kudos: 36
Kudos
Add Kudos
Bookmarks
Bookmark this Post
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 17 Jul 2025
Posts: 102,601
Own Kudos:
742,144
 [1]
Given Kudos: 98,220
Products:
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 102,601
Kudos: 742,144
 [1]
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
User avatar
luckyme17187
Joined: 07 Apr 2014
Last visit: 12 May 2015
Posts: 64
Own Kudos:
Given Kudos: 81
Posts: 64
Kudos: 118
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
8. Two marbles are drawn from a jar with 10 marbles. If all marbles are either red of blue, is the probability that both marbles selected will be red greater than 3/5?

The question: is P(R and R)=R/10*(R-1)/9>3/5?
Is R(R-1)>54?
Is R>7? (By number plugging) So, the question asks whether the number of red marbles is more than 7 (8, 9, or 10).

(1) The probability that both marbles selected will be blue is less than 1/10. This implies that B/10*(B-1)/9<1/10. So, we have that B(B-1)<9, thus B<4, so the number of red marbles in the jar is 7, 8, 9, or 10. Not sufficient.

(2) At least 60% of the marbles in the jar are red. This implies that the number of red marbles is 6 or more. Not sufficient.

(1)+(2) From above we have that R>6. Not sufficient.

Answer: E.


Hi,

Could you please help me on this..

how R(R-1)>54 turns R>7?
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 17 Jul 2025
Posts: 102,601
Own Kudos:
Given Kudos: 98,220
Products:
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 102,601
Kudos: 742,144
Kudos
Add Kudos
Bookmarks
Bookmark this Post
luckyme17187
Bunuel
8. Two marbles are drawn from a jar with 10 marbles. If all marbles are either red of blue, is the probability that both marbles selected will be red greater than 3/5?

The question: is P(R and R)=R/10*(R-1)/9>3/5?
Is R(R-1)>54?
Is R>7? (By number plugging) So, the question asks whether the number of red marbles is more than 7 (8, 9, or 10).

(1) The probability that both marbles selected will be blue is less than 1/10. This implies that B/10*(B-1)/9<1/10. So, we have that B(B-1)<9, thus B<4, so the number of red marbles in the jar is 7, 8, 9, or 10. Not sufficient.

(2) At least 60% of the marbles in the jar are red. This implies that the number of red marbles is 6 or more. Not sufficient.

(1)+(2) From above we have that R>6. Not sufficient.

Answer: E.


Hi,

Could you please help me on this..

how R(R-1)>54 turns R>7?

Bu number plugging. R is an integer, if R = 7, then R(R - 1) = 42 < 54 but if R = 8, then R(R - 1) = 56 > 54, thus R must be greater than 7.
avatar
jamescath
Joined: 05 Sep 2016
Last visit: 07 Oct 2017
Posts: 11
Own Kudos:
Given Kudos: 10
Posts: 11
Kudos: 1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
5. Set A={3-2x, 3-x, 3, 3+x, 3+2x}, where x is an integer. Is the standard deviation of set A more than the standard deviation of set B={3-2x, 3-x, 3, 3+x, 3+2x, y}

(1) The standard deviation of set A is positive. We know that the standard deviation of any set is more than or equal to zero. The standard deviation of a set is zero only when the set consists of identical elements. So, this statement implies that set A does NOT consists of identical elements or that x does not equal to zero. Still this statement is not sufficient to answer the question.

(2) y=3. The mean of set A is 3. Now, if \(x\neq{0}\) for example if x=1, then the standard deviation of B would be smaller that the standard deviation A, since the elements of B would be less widespread than the element of set A. But if x=0, then A={3, 3, 3, 3, 3} and B={3, 3, 3, 3, 3, 3}, so both will have the standard deviation of zero. Bot sufficient.

(1)+(2) Since from (1) \(x\neq{0}\), then adding a new element which equals to the mean will shrink the standard deviation, thus SD(A)>SD(B). Sufficient.

Answer: C.


I have a doubt that in set A if i substitute x as 1 and y=3 i get (1,2,3,4,5) and for set B it is (1,2,3,3,4,5) now which will have a greater standard deviation or will it be same?
Like the elements in B are more and the deviation in both sets from mean is same so B should have bigger SD but If use the logic adding nos same as mean decreases SD then Set A will have bigger SD
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 17 Jul 2025
Posts: 102,601
Own Kudos:
Given Kudos: 98,220
Products:
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 102,601
Kudos: 742,144
Kudos
Add Kudos
Bookmarks
Bookmark this Post
jamescath
Bunuel
5. Set A={3-2x, 3-x, 3, 3+x, 3+2x}, where x is an integer. Is the standard deviation of set A more than the standard deviation of set B={3-2x, 3-x, 3, 3+x, 3+2x, y}

(1) The standard deviation of set A is positive. We know that the standard deviation of any set is more than or equal to zero. The standard deviation of a set is zero only when the set consists of identical elements. So, this statement implies that set A does NOT consists of identical elements or that x does not equal to zero. Still this statement is not sufficient to answer the question.

(2) y=3. The mean of set A is 3. Now, if \(x\neq{0}\) for example if x=1, then the standard deviation of B would be smaller that the standard deviation A, since the elements of B would be less widespread than the element of set A. But if x=0, then A={3, 3, 3, 3, 3} and B={3, 3, 3, 3, 3, 3}, so both will have the standard deviation of zero. Bot sufficient.

(1)+(2) Since from (1) \(x\neq{0}\), then adding a new element which equals to the mean will shrink the standard deviation, thus SD(A)>SD(B). Sufficient.

Answer: C.


I have a doubt that in set A if i substitute x as 1 and y=3 i get (1,2,3,4,5) and for set B it is (1,2,3,3,4,5) now which will have a greater standard deviation or will it be same?
Like the elements in B are more and the deviation in both sets from mean is same so B should have bigger SD but If use the logic adding nos same as mean decreases SD then Set A will have bigger SD

The standard deviation of A should be greater than that of B. That's because we add to A an element equal to the mean of A, thus making B less widespread than A.

The SD of A = \(\sqrt{2} \approx 1.41\) and the SD of \(B = \sqrt{\frac{5}{3}} \approx 1.29\).

Please check the links below to brush up fundamentals on SD and statistics:


Hope it helps.
avatar
hannahkagalwala
Joined: 29 Nov 2016
Last visit: 01 May 2017
Posts: 5
Own Kudos:
Given Kudos: 141
Posts: 5
Kudos: 1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
9. Is x^2>2x?

Is x(x-2)>0? --> is x<0 or x>2. Basically if x is not 0, 1, or 2 we have an YES answer to the question.

(1) x is a prime number. If x=2 then the answer is NO but if x is some other prime, then the answer is YES. Not sufficient.

(2) x^2 is a multiple of 9. If x=0 then the answer is NO but if x=3, then the answer is YES. Not sufficient.

(1)+(2) Since from (1) x is a prime and from (2) x^2 is a multiple of 9, then x can only be 3. Therefore the answer to the question is YES. Sufficient.

Answer: C.


Problem with statement 2. How can 0 be a multiple of 9?
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 17 Jul 2025
Posts: 102,601
Own Kudos:
Given Kudos: 98,220
Products:
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 102,601
Kudos: 742,144
Kudos
Add Kudos
Bookmarks
Bookmark this Post
hannahkagalwala
Bunuel
9. Is x^2>2x?

Is x(x-2)>0? --> is x<0 or x>2. Basically if x is not 0, 1, or 2 we have an YES answer to the question.

(1) x is a prime number. If x=2 then the answer is NO but if x is some other prime, then the answer is YES. Not sufficient.

(2) x^2 is a multiple of 9. If x=0 then the answer is NO but if x=3, then the answer is YES. Not sufficient.

(1)+(2) Since from (1) x is a prime and from (2) x^2 is a multiple of 9, then x can only be 3. Therefore the answer to the question is YES. Sufficient.

Answer: C.


Problem with statement 2. How can 0 be a multiple of 9?

0 is not a divisor of any integer, but a multiple of every integer. So, 0 is divisible by 9: 0/9 = 0 = integer.

ZERO:

1. 0 is an integer.

2. 0 is an even integer. An even number is an integer that is "evenly divisible" by 2, i.e., divisible by 2 without a remainder and as zero is evenly divisible by 2 then it must be even.

3. 0 is neither positive nor negative integer (the only one of this kind).

4. 0 is divisible by EVERY integer except 0 itself.

Check more here: https://gmatclub.com/forum/number-proper ... 74996.html
User avatar
praveenbaranwal
Joined: 18 Feb 2018
Last visit: 21 Aug 2022
Posts: 9
Own Kudos:
Given Kudos: 7
Location: New Zealand
Concentration: Strategy, Technology
WE:Consulting (Computer Software)
Posts: 9
Kudos: 53
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
3. The length of the median BD in triangle ABC is 12 centimeters, what is the length of side AC?

(1) ABC is an isosceles triangle. Clearly insufficient.

(2) AC^2 = AB^2 + BC^2. This statement implies that ABC is a right triangle and AC is its hypotenuse. Important property: median from right angle is half of the hypotenuse, hence BD=12=AC/2, from which we have that AC=24. Sufficient.

Answer: B.

Median of a right angled triangle is half of the hypotenuse only if it is an isosceles triangle. Should this not be option C??
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 17 Jul 2025
Posts: 102,601
Own Kudos:
Given Kudos: 98,220
Products:
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 102,601
Kudos: 742,144
Kudos
Add Kudos
Bookmarks
Bookmark this Post
praveenbaranwal
Bunuel
3. The length of the median BD in triangle ABC is 12 centimeters, what is the length of side AC?

(1) ABC is an isosceles triangle. Clearly insufficient.

(2) AC^2 = AB^2 + BC^2. This statement implies that ABC is a right triangle and AC is its hypotenuse. Important property: median from right angle is half of the hypotenuse, hence BD=12=AC/2, from which we have that AC=24. Sufficient.

Answer: B.

Median of a right angled triangle is half of the hypotenuse only if it is an isosceles triangle. Should this not be option C??

The median on the hypotenuse of a right triangle ALWAYS equals one-half the hypotenuse.

To prove you can consider right triangle inscribed in a circle, where the median on the hypotenuse is radius and hypotenuse is a diameter, so the median = one-half the hypotenuse OR you can consider any rectangle, where diagonals cut each other in half: because half of the diagonal is basically the median to the another diagonal.
avatar
madzaka
Joined: 16 Dec 2019
Last visit: 16 May 2024
Posts: 54
Own Kudos:
Given Kudos: 6
Location: Bulgaria
WE:Project Management (Manufacturing)
Posts: 54
Kudos: 24
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
SOLUTION:

1. What is the product of three consecutive integers?

(1) At least one of the integers is positive.

We can have three cases:
(i) All three integers are positive. In this case the product will obviously be positive.
(ii) Two of the integers are positive: {0, 1, 2}. In this case the product will be zero.
(iii) Only one of the integers is positive: {-1, 0, 1}. In this case the product will be zero.

Not sufficient.

(2) The sum of the integers is less than 6. Clearly insufficient, consider {-1, 0, 1} and {-3, -2, -1}.

(1)+(2) The second statement implies that we cannot have case (i) from (1), since the least sum of three positive consecutive integers is 1+2+3=6. Thus we have either case (ii) or case (iii). Therefore the product of the integers is zero. Sufficient.

Answer: C.

What is the problem with 0,1,2? isn't it also an answer and thus even both together can't answer the question
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 17 Jul 2025
Posts: 102,601
Own Kudos:
742,144
 [1]
Given Kudos: 98,220
Products:
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 102,601
Kudos: 742,144
 [1]
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
madzaka
Bunuel
SOLUTION:

1. What is the product of three consecutive integers?

(1) At least one of the integers is positive.

We can have three cases:
(i) All three integers are positive. In this case the product will obviously be positive.
(ii) Two of the integers are positive: {0, 1, 2}. In this case the product will be zero.
(iii) Only one of the integers is positive: {-1, 0, 1}. In this case the product will be zero.

Not sufficient.

(2) The sum of the integers is less than 6. Clearly insufficient, consider {-1, 0, 1} and {-3, -2, -1}.

(1)+(2) The second statement implies that we cannot have case (i) from (1), since the least sum of three positive consecutive integers is 1+2+3=6. Thus we have either case (ii) or case (iii). Therefore the product of the integers is zero. Sufficient.

Answer: C.

What is the problem with 0,1,2? isn't it also an answer and thus even both together can't answer the question

{0, 1, 2} is the only set possible --> the product is 0.
User avatar
Dyaneth
Joined: 13 Oct 2021
Last visit: 21 Dec 2024
Posts: 5
Own Kudos:
Given Kudos: 186
Posts: 5
Kudos: 18
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
6. The ratio of the number of employees of three companies X, Y, and Z is 3:4:8, respectively. Is the average age of all employees in these companies less than 40 years?

Given that the ratio of the number of employees is \(3x:4x:8x\) for some positive multiple \(x\).

The question asks whether the average age, which is equal to \(\frac{(total \ age)}{(number \ of \ employees)} < 40\). This is equivalent to asking whether \(\frac{(total \ age)}{3x+4x+8x} < 40\), or in other words: is \((total \ age) < 600x\)?

(1) The total age of all the employees in these companies is 600 years.

The question simplifies to: is \(600 < 600x\)? Or equivalently, is \(1 < x\)?

We do not know that: if \(x=1\), then the answer is NO, but if \(x > 1\), then the answer is YES. Not sufficient.

(2) The average age of employees in X, Y, and Z, is 40, 20, and 50 years, respectively.

The above implies that \((total \ age)=40*3x+20*4x+50*8x=600x\), so the answer to the question is NO. Sufficient.


Answer: B
­Thank you so much for the questions and answers!

Given that the ratio of the number of employees is \(3x:4x:8x\) for some positive multiple \(x\)., why is it wrong to assume that x has to be 1 or greater than 1?
After all, we are talking about people here and the number of employees has to be an integer number.

Thanks in advance!
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 17 Jul 2025
Posts: 102,601
Own Kudos:
Given Kudos: 98,220
Products:
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 102,601
Kudos: 742,144
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Dyaneth
Bunuel
6. The ratio of the number of employees of three companies X, Y, and Z is 3:4:8, respectively. Is the average age of all employees in these companies less than 40 years?

Given that the ratio of the number of employees is \(3x:4x:8x\) for some positive multiple \(x\).

The question asks whether the average age, which is equal to \(\frac{(total \ age)}{(number \ of \ employees)} < 40\). This is equivalent to asking whether \(\frac{(total \ age)}{3x+4x+8x} < 40\), or in other words: is \((total \ age) < 600x\)?

(1) The total age of all the employees in these companies is 600 years.

The question simplifies to: is \(600 < 600x\)? Or equivalently, is \(1 < x\)?

We do not know that: if \(x=1\), then the answer is NO, but if \(x > 1\), then the answer is YES. Not sufficient.

(2) The average age of employees in X, Y, and Z, is 40, 20, and 50 years, respectively.

The above implies that \((total \ age)=40*3x+20*4x+50*8x=600x\), so the answer to the question is NO. Sufficient.


Answer: B
­Thank you so much for the questions and answers!

Given that the ratio of the number of employees is \(3x:4x:8x\) for some positive multiple \(x\)., why is it wrong to assume that x has to be 1 or greater than 1?
After all, we are talking about people here and the number of employees has to be an integer number.

Thanks in advance!
­
That's exactly the case: x can be 1, and in the case the answer is NO, and it can be more than 1, say 2, and in this case the answer is YES.­
User avatar
einstein801
Joined: 23 Jan 2024
Last visit: 18 Feb 2025
Posts: 180
Own Kudos:
Given Kudos: 138
Posts: 180
Kudos: 136
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Looking for a DS probability trap question which goes something like this, can anyone help?

What is the probability of event X happening?

1) Probability of event X not happening is 0.2
2) Probability of event X happening is 0.8
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 17 Jul 2025
Posts: 102,601
Own Kudos:
Given Kudos: 98,220
Products:
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 102,601
Kudos: 742,144
Kudos
Add Kudos
Bookmarks
Bookmark this Post
unicornilove
Looking for a DS probability trap question which goes something like this, can anyone help?

What is the probability of event X happening?

1) Probability of event X not happening is 0.2
2) Probability of event X happening is 0.8
­Check these:
https://gmatclub.com/forum/if-event-a-a ... 90932.html
https://gmatclub.com/forum/events-a-and ... 68076.html
https://gmatclub.com/forum/let-s-be-a-s ... 05932.html
https://gmatclub.com/forum/when-a-rando ... 01785.html

Hope this helps.
 
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 37,434
Own Kudos:
Posts: 37,434
Kudos: 1,013
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
   1   2   3 
Moderators:
Math Expert
102601 posts
453 posts