Set S consists of five consecutive integers and set T consists of seven consecutive integers. Is the median of the numbers in set S equal to the median of the numbers in set T?
(1) The median of the numbers in set S is 0.
(2) The sum of numbers in set S is equal to the sum of numbers in set T.
Set S consists of five consecutive integers and set T consists of seven consecutive integers. Is the median of the numbers in set S equal to the median of the numbers in set T?
(1) The median of the numbers in set S is 0.
(2) The sum of numbers in set S is equal to the sum of numbers in set T.
C.
Whats the OA ?
Can you plz explain how you arrived at answer choice (C)? Thanks a lot.
Quote:
Originally Posted by *arch* View Post
Set S consists of five consecutive integers and set T consists of seven consecutive integers. Is the median of the numbers in set S equal to the median of the numbers in set T?
(1) The median of the numbers in set S is 0.
(2) The sum of numbers in set S is equal to the sum of numbers in set T.
Set S consists of five consecutive integers and set T consists of seven consecutive integers. Is the median of the numbers in set S equal to the median of the numbers in set T?
(1) The median of the numbers in set S is 0.
(2) The sum of numbers in set S is equal to the sum of numbers in set T.
Shouldn't the answer be B as I think option B is sufficient to say that the median should be 0 as in other cases the sum of 5 consecutive integers can't be equal to sum of 7 consecutive integers. Please correct me if I am wrong.
Arch - Whats the OA ?
I chose (B) as well.. but the OA is (C). This question came in one of the GMAT Prep Practice tests.
Shouldn't the answer be B as I think option B is sufficient to say that the median should be 0 as in other cases the sum of 5 consecutive integers can't be equal to sum of 7 consecutive integers. Please correct me if I am wrong.
Arch - Whats the OA ?
*arch* SaysI chose (B) as well.. but the OA is (C). This question came in one of the GMAT Prep Practice tests.
By the time some excellent puy will enlighten us, is there any explanation given in Gmatprep for this problem ?
Dopa SaysBy the time some excellent puy will enlighten us, is there any explanation given in Gmatprep for this problem ?
suppose the first no of both sets S and T are a and b respectively.
then by stem 2..
5a + 10 = 7b + 10
=> a =(7/5)*b
Hence we cannot be sure that the median will be zero..
As per your guess, -7 and -5 do satisfy this equation making median zero..
but 14 and 10 also do..
because 14 , 15, 16, 17, 18 have sum = 80 and median = 16
and 10, 11, 12, 13, 14, 15, 16 also have sum =80 but median = 13
Q.1) If 2 different representatives are to be selected at random from a group of 10 employees and if p is the probability that both representatives selected will be women, is p > 1/2?
(1) More than 1/2 of the 10 employees are women.
(2) The probability that both representatives selected will be men is less than 1/10.
q.2) If n is a positive integer and r is the remainder when (n 1)(n + 1) is divided by 24, what is the value of r?
(1) 2 is not a factor of n.
(2) 3 is not a factor of n.
(1) More than 1/2 of the 10 employees are women.
(2) The probability that both representatives selected will be men is less than 1/10.
q.2) If n is a positive integer and r is the remainder when (n 1)(n + 1) is divided by 24, what is the value of r?
(1) 2 is not a factor of n.
(2) 3 is not a factor of n.
suppose the first no of both sets S and T are a and b respectively.
then by stem 2..
5a + 10 = 7b + 10
=> a =(7/5)*b
Hence we cannot be sure that the median will be zero..
As per your guess, -7 and -5 do satisfy this equation making median zero..
but 14 and 10 also do..
because 14 , 15, 16, 17, 18 have sum = 80 and median = 16
and 10, 11, 12, 13, 14, 15, 16 also have sum =80 but median = 13
Dude, it seems there is some confusion.
Sum of 14 , 15, 16, 17, 18 is definitely 80 but sum of 10, 11, 12, 13, 14, 15, 16 is 91.
Q.1) If 2 different representatives are to be selected at random from a group of 10 employees and if p is the probability that both representatives selected will be women, is p > 1/2?
(1) More than 1/2 of the 10 employees are women.
(2) The probability that both representatives selected will be men is less than 1/10.
q.2) If n is a positive integer and r is the remainder when (n 1)(n + 1) is divided by 24, what is the value of r?
(1) 2 is not a factor of n.
(2) 3 is not a factor of n.
I think the 1st question has already being discussed if you'll try to flicker few pages back. Here is my answer and explanation for the 2nd one -
2. (n 1)(n + 1) i.e. (n^2 -1) is divided by 24, what is the value of r ?
Option 1 : 2 is not a factor of n. That means n can be 1, 3, 9 etc...all give a different value of remanider. Not sufficient.
Option 2 : 3 is not a factor of n. That means n can be 1, 2, 5, etc...all give a different value of remanider. Not sufficient.
Option 1 and 2 simultaneously : 2 and 3 both are not a factor of n. That means n can be 1, 5, 7, 11, 13 etc...all give the same value of remanider r as 0 when (n^2 -1) is divided by 24.
C should be the answer.
Whats the OA ?
Dude, it seems there is some confusion.
Sum of 14 , 15, 16, 17, 18 is definitely 80 but sum of 10, 11, 12, 13, 14, 15, 16 is 91.
ya,
I made a wrong equation :(
5a + 10 = 7b + 21
a = (7b + 11)/5
hence b = -3 and a =-2 is a solution. making median zero.
But also b = 2 and a = 5 is also solution meaning
S = {5, 6, 7, 8, 9} sum = 35 median = 7
T = {2, 3, 4, 5, ,6 7, 8} sum = 25 median = 5.
Hence we cannot be sure and B is insufficient.
Sorry for the goofup.
Can someone explain the answers to the foll. questions?
1.Is quadrilateral RSTV a rectangle?
- The measure of RST is 90o
- The measure of TVR is 90o
2. If x0, is x| (1) x2(2) |x
Can someone explain the answers to the foll. questions?
1.Is quadrilateral RSTV a rectangle?
- The measure of RST is 90o
- The measure of TVR is 90o
2. If x0, is x| (1) x2(2) |x
E and D.
Whats the OA?
Can someone explain the answers to the foll. questions?
1.Is quadrilateral RSTV a rectangle?
- The measure of RST is 90o
- The measure of TVR is 90o
2. If x0, is x| (1) x2(2) |x
Q1) E as a quadrilateral is possible which can neither be a sq nor a rectangle
Q2) A
wat r the OAs?
My answers would be
1)C
2)D
Ans 1
1) Insufficient: We cant say anything about more than 1 angle of the quadrilateral.
2) Insufficient: We cant say anything about more than 1 angle of the quadrilateral.
Even after combining both the statements, we can only say that allangles are 90. It could also be a square and not neccesarily rectangle. Thus, E
However, another line of thinking is, since every square is a rectangle, thus RSTV is a rectangle. Thus, C
Quite confusing
Ans 2)
1) Sufficient: x^2 -12) Sufficient: Since, x is always positive, we can say that x>0
Thus, this equation also maps to x^20, giving us
0
@ ankit,
Q1) U can draw a quadrilateral where
If this condition is true, mod(x)
hence D
i'm sorry i posted the wrong ans for Q2 as A earlier but its actually its C
dear raj, wat r the OAs?
thanks
I think the 1st question has already being discussed if you'll try to flicker few pages back. Here is my answer and explanation for the 2nd one -
2. (n 1)(n + 1) i.e. (n^2 -1) is divided by 24, what is the value of r ?
Option 1 : 2 is not a factor of n. That means n can be 1, 3, 9 etc...all give a different value of remanider. Not sufficient.
Option 2 : 3 is not a factor of n. That means n can be 1, 2, 5, etc...all give a different value of remanider. Not sufficient.
Option 1 and 2 simultaneously : 2 and 3 both are not a factor of n. That means n can be 1, 5, 7, 11, 13 etc...all give the same value of remanider r as 0 when (n^2 -1) is divided by 24.
C should be the answer.
Whats the OA ?
Yeah C is the answer. Thanks.
@ ankit,
Q1) U can draw a quadrilateral whereThis condition is possible when x=1/a, where a >0
If this condition is true, mod(x)
hence D
i'm sorry i posted the wrong ans for Q2 as A earlier but its actually its C
dear raj, wat r the OAs?
thanks
your answers are right.The OA are E,D
I was wondering why cant 1 be C and 2 be A.
1.C ,because I assumed square is also a rectange
and
2.A ,because of the below reasoning.Pls correct me here..
a) sufficient
b)
x
x = x^2 x^2 > -1 (insufficient)
My answers would be
1)C
2)D
Ans 1
1) Insufficient: We cant say anything about more than 1 angle of the quadrilateral.
2) Insufficient: We cant say anything about more than 1 angle of the quadrilateral.
Even after combining both the statements, we can only say that allangles are 90. It could also be a square and not neccesarily rectangle. Thus, E
However, another line of thinking is, since every square is a rectangle, thus RSTV is a rectangle. Thus, C
Quite confusing
Ans 2)
1) Sufficient: x^2 -12) Sufficient: Since, x is always positive, we can say that x>0
Thus, this equation also maps to x^20, giving us
0
Ankit,
In your reasoning,
2) Sufficient: Since, x is always positive, we can say that x>0
Thus, this equation also maps to x^20, giving us
0
I agree |x is always +ve,but how did u conclude x>0?
-Rajk
(Always had trouble with mods)
1) Set S has five numbers and have a median zero. That means there are 2 numbers which are less than zero, two which are greater than zero and one equal to zero. Since all numbers are consecutive, the numbers could only be -2,-1,0,1,2, which also makes sum of numbers as zero.
But since we have no info about T, insufficient.
2) We cant comment on medians of two sets on the basis of sum of numbers on the set alone. Insufficient
On combining the two, we get that Sum of numbers in set T is also zero. And since T also has an odd number of elements ( seven here) and all are consecutive, the numbers have to be -3,-2,-1,0,1,2,3 and thus median is 0.
Answer is C :)
Ankit,
Could you please help me understanding as why not option 2 is sufficient. I thought that if sum of 5 consecutive numbers is equal to sum of 7 consecutive numbers then its only possible when both sets have median as zero i.e. both the sets should be symmetric about 0.
Please point out as where am I going wrong.
Thanks!
I beg to differ from you. A quadrilateral RSTV, with its corners named R,S,T,V in this order and with given given conditions has to be a rectangle/square. Try making a pencil sketch of what you are trying to say. Im sure u wudnt be able to.
At least I wasnt able to do so.
May be ur drawing wud help me clear some fundas :)
My first choice was also E and it still could be E....all im trying to say is that with the given conditions, you wud definately get a quad having all its angles as 90
Ankit,
For a quadrilateral to become a parallelogram(here rectangle) opposite angles should be equal and adjacent angles should be complimentary.Here we can say only that angle S = angle V =90 so angle R+angle T =180 but we are not told that side RS parallel to VT or RV parallel to ST. so hw can we conclude that R = angle T =90 or it can be any two angles whose sum can be 180.
Pls correct me if i'm wrong........