Data Sufficiency

1. If Bob makes 36 or fewer items in a week, he is paid x dollars per item. If Bob produces more than 36 items in a week, he is paid x dollars per item for 1st 36 and 1.5x for each additional item. How many items did he produce last week?
a. Last week Bob was paid a total of $480
b. This week Bob made 2 more items than last week and was paid a total of $150

2. For the set on n numbers where n > 1, is the average equal to the median?
a. If n is listed in increasing order, then the difference between any pair of successive numbers is 2
b. The range of the n numbers in the set is 2(n-1)

3. Distance between x and y is greater than distance between x and z. Does z lie between x and y on the number line?
a. xyz < 0
b. xy < 0

4. Jan has only b black, w white and r red marbles. If 1 marble is chosen at random, is probability that the marble chosen will be red greater than probability that marble chosen is white?
a. r/b+w > w/b+r
b. b-w > r

Regards

DREAM GMAT wrote:1. If Bob makes 36 or fewer items in a week, he is paid x dollars per item. If Bob produces more than 36 items in a week, he is paid x dollars per item for 1st 36 and 1.5x for each additional item. How many items did he produce last week?
a. Last week Bob was paid a total of $480
b. This week Bob made 2 more items than last week and was paid a total of $150

2. For the set on n numbers where n > 1, is the average equal to the median?
a. If n is listed in increasing order, then the difference between any pair of successive numbers is 2
b. The range of the n numbers in the set is 2(n-1)

3. Distance between x and y is greater than distance between x and z. Does z lie between x and y on the number line?
a. xyz < 0
b. xy < 0

4. Jan has only b black, w white and r red marbles. If 1 marble is chosen at random, is probability that the marble chosen will be red greater than probability that marble chosen is white?
a. r/b+w > w/b+r
b. b-w > r

Regards

1: You've made a mistake transcribing this problem, since as written, this week he made more items but earned less money! I suspect it should be 510?

2: 1 alone is sufficient; for ANY list where all the terms increase by the same interval, the median and average are always that same. 2 is useless, because the range of a list tells us nothing of the numbers in the middle. A

3: The only information we get with both statements is the X and Y have opposite signs, and that when combined we know Z must be positive. On first glance this looks bad, but when in doubt we can confirm by picking numbers.

x = -1 y = 7 z = 2
Y is further from X than is Z, and Z is between X and Y.
x = 1 y = -7 z = 2
Y is further from X than is Z, and Z is NOT between them.
These numbers work even with both statements. E


4: We are asking for whether the probability of r is greater than the of w. Since the number of marbles is constant, we cancel it out and end up asking if r > w.

1) r/b + w > w/b + r
Multiply everything by b (which we know is positive)
r + wb > w + rb
Get the Rs and Ws alone
wb - w > rb - r
Factor
w(b-1) > r(b-1)
b cannot equal one because that would make this statement false, and b is a positive integer, so b must be at least 2 and b-1 must be positive. Divide w/out flipping signs

w > r; the answer is No, which is sufficient.

2) b-w > r can be rewritten as b-r > w. In other words, it tells us nothing about the relationships between r and w.

A; 1 is sufficient.

KapTeacherEli wrote:

DREAM GMAT wrote:1. If Bob makes 36 or fewer items in a week, he is paid x dollars per item. If Bob produces more than 36 items in a week, he is paid x dollars per item for 1st 36 and 1.5x for each additional item. How many items did he produce last week?
a. Last week Bob was paid a total of $480
b. This week Bob made 2 more items than last week and was paid a total of $150

2. For the set on n numbers where n > 1, is the average equal to the median?
a. If n is listed in increasing order, then the difference between any pair of successive numbers is 2
b. The range of the n numbers in the set is 2(n-1)

3. Distance between x and y is greater than distance between x and z. Does z lie between x and y on the number line?
a. xyz < 0
b. xy < 0

4. Jan has only b black, w white and r red marbles. If 1 marble is chosen at random, is probability that the marble chosen will be red greater than probability that marble chosen is white?
a. r/b+w > w/b+r
b. b-w > r

Regards

1: You've made a mistake transcribing this problem, since as written, this week he made more items but earned less money! I suspect it should be 510?

2: 1 alone is sufficient; for ANY list where all the terms increase by the same interval, the median and average are always that same. 2 is useless, because the range of a list tells us nothing of the numbers in the middle. A

3: The only information we get with both statements is the X and Y have opposite signs, and that when combined we know Z must be positive. On first glance this looks bad, but when in doubt we can confirm by picking numbers.

x = -1 y = 7 z = 2
Y is further from X than is Z, and Z is between X and Y.
x = 1 y = -7 z = 2
Y is further from X than is Z, and Z is NOT between them.
These numbers work even with both statements. E


4: We are asking for whether the probability of r is greater than the of w. Since the number of marbles is constant, we cancel it out and end up asking if r > w.

1) r/b + w > w/b + r
Multiply everything by b (which we know is positive)
r + wb > w + rb
Get the Rs and Ws alone
wb - w > rb - r
Factor
w(b-1) > r(b-1)
b cannot equal one because that would make this statement false, and b is a positive integer, so b must be at least 2 and b-1 must be positive. Divide w/out flipping signs

w > r; the answer is No, which is sufficient.

2) b-w > r can be rewritten as b-r > w. In other words, it tells us nothing about the relationships between r and w.

A; 1 is sufficient.

Thanks Eli for your explanations.

I still have some doubts i writing them wrt to questions

1. You correct there is some problem with statement 2 , even realized when i was doing the question n answer. But there no mistake in the question.
The source for these questions is : https://www.beatthegmat.com/198-level-70 ... 43783.html

2. Thanks for clarifying the Statement 2.

3. I agree with your explanation i did the same but the answer specified in answer key is "C". The source of question is same as mentioned above.

4. In this i have a doubt in your clarification.
In first step u have mentioned to multiply everything by "b". I did the same but was not able to deduce the expression to r+wb > w+rb.
Kindly explain your deduction.

Thanks

Mandeep

DREAM GMAT wrote: Thanks Eli for your explanations.

I still have some doubts i writing them wrt to questions

1. You correct there is some problem with statement 2 , even realized when i was doing the question n answer. But there no mistake in the question.
The source for these questions is : https://www.beatthegmat.com/198-level-70 ... 43783.html

2. Thanks for clarifying the Statement 2.

3. I agree with your explanation i did the same but the answer specified in answer key is "C". The source of question is same as mentioned above.

4. In this i have a doubt in your clarification.
In first step u have mentioned to multiply everything by "b". I did the same but was not able to deduce the expression to r+wb > w+rb.
Kindly explain your deduction.

Thanks

Mandeep

1: It's clearly intended to by 510. The answer, by the way, would be E; with both statements, he could have created 32 the first week at 15 each, and 34 the second week, and X is 15; or, he could have made 44 the first week at x=10 and x+50% at 15, earning another 30 dollars week 2 with a total of 46 items.

3: It's possible I'm missing something, but as we have two sets of numbers that satisfy both statements and give conflicting answers, I suspect the source is in error. If I'm wrong, though, i'd love to know how!

4:
r/b + w > w/b + r
b(r/b + w) > b(w/b + r)
b(r/b) + b(w) > b(w/b) + b(r)
r + wb > w + rb