My answer is (A) - Statement 1 alone is Sufficient. Here's my reasoning:-
Given=gcd of a & b = g; numbers can be assumed to be gX and gY ;therefore gcd of ma and nb => gcd of mgX and ngY.
Statement (1) says gcd of m & n = 1; as gX & gY have g in common; and m & n are co-primes, one can conclude that gcd of m & n = g. Hence Statement (1) is SUFFICIENT
Statement (2) says b = 3m+1 & n=a-1; therefore ma = 3mgX & nb = ngy. gX & gY have g in common - so we need to find the gcd of 3m and n. (they can be expressed as --> 3m=gY+1 and n=gX+1). The relationship between the 3m and n cannot be concluded from this. Hence Statement (2) is NOT SUFFICIENT
jha16june SaysCan any one solve this now. It has already been solved partially.
The gcd of a nd b is g. If a, b, m, and n are all positive integers, what is the gcd of ma and nb?
1. gcd of m and n is 1.
2. b=3m+1 and n = a-1.
as per my solution this can be answered by 1st statement only.
Detailed solution
let a = p*g and b = q*g (as g is GCD)
now take first statement
it implies m = I*x and n= I*y (I is GCD)
now ma = pIgx and nb = qygI
and from above gcd of ma and nb = Ig
now lets take second statement:
b=3m+I => nb = n(3m+I)
n=a-I +> a = n+I => ma = m(n+I)
hence we can not decide gcd of ma,nb based on second statement
someone please verify it..........
If r & s are positive integers, is r/s an integer?
(1) every factor of s is also a factor of r.
(2) every prime factor of s is also a prime factor of r.
--------------------------------------------------
I Z^n = 1 (^ denotes power or exponent), what is the value of z?
(1) n is a nonzero integer
(2) z>0
--------------------------------------------------
If you know the answers for these questions, can you post them along with your reasoning?
Thanks a lot =]
If r & s are positive integers, is r/s an integer?
(1) every factor of s is also a factor of r.
(2) every prime factor of s is also a prime factor of r.
--------------------------------------------------
I Z^n = 1 (^ denotes power or exponent), what is the value of z?
(1) n is a nonzero integer
(2) z>0
--------------------------------------------------
If you know the answers for these questions, can you post them along with your reasoning?
Thanks a lot =]
For the first question I think the ans is A.
Is that the ans?
Reasoning
For the first condition to occur 's' itself to be a factor of 'r'.so always r/s is an integer.I think so..........criticisms are welcome.
for eg: take r=12 so factors are 1,2,3,4,6,12
take s= 2 ,so r/s is an integer
take s=6 ,so r/s is an integer
take s=9 ,(we cant take 9 b/c factors are not same)r/s is not an integer.
Take second condition
Here r=12 then prime factors of r are 2,3
take s=9 pf is 3 the condition is satisfied but r/s is not an integer.
take s=4 pf is 2 the condition is satisfied and r/s is an integer.
So 2nd condition cant be used for reasoning.
for second Q is there an 'I' in it?
If r & s are positive integers, is r/s an integer?
(1) every factor of s is also a factor of r.
(2) every prime factor of s is also a prime factor of r.
--------------------------------------------------
I Z^n = 1 (^ denotes power or exponent), what is the value of z?
(1) n is a nonzero integer
(2) z>0
--------------------------------------------------
If you know the answers for these questions, can you post them along with your reasoning?
Thanks a lot =]
1st Q:
Answer is A, cos s is also a factor of s, so s is a factor of r too.
and B is not sufficient, as non prime factor are not in r.
2nd Q:
if n =2, then z can be +1 or -1. So not so not sufficient.
if z>1, then for z=1, any real number will do, and also for n =0, ne real z will do. So B is not sufficient.
Together yes we can say theat z=1. So C is the answer.
The gcd of a nd b is g. If a, b, m, and n are all positive integers, what is the gcd of ma and nb?
1. gcd of m and n is 1.
2. b=3m+1 and n = a-1.
as per my solution this can be answered by 1st statement only.
Detailed solution
let a = p*g and b = q*g (as g is GCD)
now take first statement
it implies m = I*x and n= I*y (I is GCD)
now ma = pIgx and nb = qygI
and from above gcd of ma and nb = Ig
now lets take second statement:
b=3m+I => nb = n(3m+I)
n=a-I +> a = n+I => ma = m(n+I)
hence we can not decide gcd of ma,nb based on second statement
someone please verify it..........
Inder bhai there is a basic concept:
if gcd(a,b) is g then a=gm and b = gn where gcd(m, n)=1. Also read other posts on this question.
Inder bhai there is a basic concept:
if gcd(a,b) is g then a=gm and b = gn where gcd(m, n)=1. Also read other posts on this question.
Does it mean that what i have solved is wrong(i took first statement as
gcd of m nd n is I (not one) by mistake)
Hi,
Attached are a couple of GMAT Prep DS questions which I got wrong..
Can somebody please explain these.
Thanks,
Aakash
Question (2)
As per the question when the tree is planted it is 4ft tall. After which it grows
at a uniform rate.
0th year --> 4 ft
1st year --> 4+x
2nd year --> 4+2x
3rd year --> 4+3x
4th year --> 4+4x
5th year --> 4+5x
6th year --> 4+6x
It is given that at the end of the 6th year, the tree was 1/5th taller
than it was at the end of the 4th year.
--> 4+6x = 1/5 (4+4x) + (4+4x)
Solve to get x = 2/3
ANSWER IS 2/3.
------------------------------------------------------------
Question (1):-
Statement 1 ->16 students at the school study both French and Japanese.
This only tells that 16= 4/100 (Total Students). We will therefore we be able to find the Total Number of Students as 400. However, this is NOT SUFFICIENT as it does not provide us any information about how many french students are there to compare with the no. of japanese students.
Statement 2 -> 10 percent of the students at the school who study japanese also study french. This statement is SUFFICIENT. Reasoning given below:-
10/100 (Japanese Students) = 4/100 (French Students)
--> J = 4F
This information is sufficient to find out which number of students is higher.
(Note the 4/100 (french students) is already given in the question).
ANSWER IS (B) - STATEMENT 2 ALONE IS SUFFICIENT.
----------------------------------------------------------------------
As per the question when the tree is planted it is 4ft tall. After which it grows
at a uniform rate.
0th year --> 4 ft
1st year --> 4+x
2nd year --> 4+2x
3rd year --> 4+3x
4th year --> 4+4x
5th year --> 4+5x
6th year --> 4+6x
It is given that at the end of the 6th year, the tree was 1/5th taller
than it was at the end of the 4th year.
--> 4+6x = 1/5 (4+4x) + (4+4x)
Solve to get x = 2/3
ANSWER IS 2/3.
------------------------------------------------------------
Question (1):-
Statement 1 ->16 students at the school study both French and Japanese.
This only tells that 16= 4/100 (Total Students). We will therefore we be able to find the Total Number of Students as 400. However, this is NOT SUFFICIENT as it does not provide us any information about how many french students are there to compare with the no. of japanese students.
Statement 2 -> 10 percent of the students at the school who study japanese also study french. This statement is SUFFICIENT. Reasoning given below:-
10/100 (Japanese Students) = 4/100 (French Students)
--> J = 4F
This information is sufficient to find out which number of students is higher.
(Note the 4/100 (french students) is already given in the question).
ANSWER IS (B) - STATEMENT 2 ALONE IS SUFFICIENT.
----------------------------------------------------------------------
Question (2)
As per the question when the tree is planted it is 4ft tall. After which it grows
at a uniform rate.
0th year --> 4 ft
1st year --> 4+x
2nd year --> 4+2x
3rd year --> 4+3x
4th year --> 4+4x
5th year --> 4+5x
6th year --> 4+6x
It is given that at the end of the 6th year, the tree was 1/5th taller
than it was at the end of the 4th year.
--> 4+6x = 1/5 (4+4x) + (4+4x)
Solve to get x = 2/3
ANSWER IS 2/3.
------------------------------------------------------------
Question (1):-
Statement 1 ->16 students at the school study both French and Japanese.
This only tells that 16= 4/100 (Total Students). We will therefore we be able to find the Total Number of Students as 400. However, this is NOT SUFFICIENT as it does not provide us any information about how many french students are there to compare with the no. of japanese students.
Statement 2 -> 10 percent of the students at the school who study japanese also study french. This statement is SUFFICIENT. Reasoning given below:-
10/100 (Japanese Students) = 4/100 (French Students)
--> J = 4F
This information is sufficient to find out which number of students is higher.
(Note the 4/100 (french students) is already given in the question).
ANSWER IS (B) - STATEMENT 2 ALONE IS SUFFICIENT.
----------------------------------------------------------------------
Thanks a lot for your explanation
For the 1st question i thought 4+6x = 1/5 (4+4x) equation applies... just got corrected
Pls solve...
If vmt 0, is v2m3t-4 > 0?
(1) m > v2
(2) m > t-4
pls read v2 as 'v' to the power of 2 ,m3 as m to the power of 3 and 't-4' as 't' to the power of -4.
Is the Answer "D" ?!?! My reasoning is as follows:- (Plz correct me if i'm wrong!)
V2 is always positive; and t-4 is also always positive; hence the answer only depends on "m" being positive of negative.
(1) Statement 1 says m>v2
V2 is always positive; and t-4 is also always positive; since m>v2; m3 is definitely positive; therefore v2m3t-4 >0
(2) Statement 2 says m > t-4
v2, t-4 are always positive; as it is given that m>t-4, m3 will definitely be positive; therefore v2m3t-4 >0
Both statements can independently answer the question; so answer is D.
----------------
Pls solve...
If vmt 0, is v2m3t-4 > 0?
(1) m > v2
(2) m > t-4
pls read v2 as 'v' to the power of 2 ,m3 as m to the power of 3 and 't-4' as 't' to the power of -4.
It is 'D' ..thanks a lot for the explanation!
Is the Answer "D" ?!?! My reasoning is as follows:- (Plz correct me if i'm wrong!)
V2 is always positive; and t-4 is also always positive; hence the answer only depends on "m" being positive of negative.
(1) Statement 1 says m>v2
V2 is always positive; and t-4 is also always positive; since m>v2; m3 is definitely positive; therefore v2m3t-4 >0
(2) Statement 2 says m > t-4
v2, t-4 are always positive; as it is given that m>t-4, m3 will definitely be positive; therefore v2m3t-4 >0
Both statements can independently answer the question; so answer is D.
----------------
Does it mean that what i have solved is wrong(i took first statement as
gcd of m nd n is I (not one) by mistake)
The answer to this question is C, we can answer only with the help of both the statement. I have already replied why the 1st stmt alone is not sufficient.
Answer is D (Both are not sufficient to answer the question) Since its also possible he worked
Mon-8
Tue-8
Wed-8
Thr-7
Fri-7
Sat-8
Sun-8
Hi.. Can someone please help me answer these questions? Thanks a ton!
Each of the 45 boxes on shelf J weighs less than each of the 44 boxes on Shelf K. What is the median weight of the 89 boxes on these shelves?
(1) The heaviest box on shelf J weighs 15 pounds.
(2) The lightest box on shelf K weighs 20 pounds.
-------------------------------------------------------------------
Each week a certain salesman made a fixed amount equal to $300 plus a commission equal to 5 percent of the amount of these sales that week over $1000. What is the total amount the salesman was paid last week?
(1) The total amount the salesman was paid last week is equal to 10 percent of the amount of these sales last week.
(2) The salesman's sales last week total to $5000.
-------------------------------------------------------------------
If the line k in the xy-plane has equation y=mx +b, where m and b are constants, what is the slope of k?
(1) k is parallel to the line with equation y = (1-m)x+b+1
(2) k intersects the line with equation y = 2x+3 at the point (2,7).
--------------------------------------------------------------------
Each of the 45 boxes on shelf J weighs less than each of the 44 boxes on Shelf K. What is the median weight of the 89 boxes on these shelves?
(1) The heaviest box on shelf J weighs 15 pounds.
(2) The lightest box on shelf K weighs 20 pounds.
-------------------------------------------------------------------
Each week a certain salesman made a fixed amount equal to $300 plus a commission equal to 5 percent of the amount of these sales that week over $1000. What is the total amount the salesman was paid last week?
(1) The total amount the salesman was paid last week is equal to 10 percent of the amount of these sales last week.
(2) The salesman's sales last week total to $5000.
-------------------------------------------------------------------
If the line k in the xy-plane has equation y=mx +b, where m and b are constants, what is the slope of k?
(1) k is parallel to the line with equation y = (1-m)x+b+1
(2) k intersects the line with equation y = 2x+3 at the point (2,7).
--------------------------------------------------------------------
Hi.. Can someone please help me answer these questions? Thanks a ton!
Each of the 45 boxes on shelf J weighs less than each of the 44 boxes on Shelf K. What is the median weight of the 89 boxes on these shelves?
(1) The heaviest box on shelf J weighs 15 pounds.
(2) The lightest box on shelf K weighs 20 pounds.
-------------------------------------------------------------------
Each week a certain salesman made a fixed amount equal to $300 plus a commission equal to 5 percent of the amount of these sales that week over $1000. What is the total amount the salesman was paid last week?
(1) The total amount the salesman was paid last week is equal to 10 percent of the amount of these sales last week.
(2) The salesman's sales last week total to $5000.
-------------------------------------------------------------------
If the line k in the xy-plane has equation y=mx +b, where m and b are constants, what is the slope of k?
(1) k is parallel to the line with equation y = (1-m)x+b+1
(2) k intersects the line with equation y = 2x+3 at the point (2,7).
--------------------------------------------------------------------
For 2nd question ans is B......pls confirm?
Hi.. Can someone please help me answer these questions? Thanks a ton!
Each of the 45 boxes on shelf J weighs less than each of the 44 boxes on Shelf K. What is the median weight of the 89 boxes on these shelves?
(1) The heaviest box on shelf J weighs 15 pounds.
(2) The lightest box on shelf K weighs 20 pounds.
Answer is 1. When u sort the data the 45th(middle term of 89) box weighs 15 pounds.
-------------------------------------------------------------------
Each week a certain salesman made a fixed amount equal to $300 plus a commission equal to 5 percent of the amount of these sales that week over $1000. What is the total amount the salesman was paid last week?
(1) The total amount the salesman was paid last week is equal to 10 percent of the amount of these sales last week.
(2) The salesman's sales last week total to $5000.
Answer is D:
1. => 300+ (T-1000)*.05= 0.1*T
2. => 300 + (5k-1k)*.05
-------------------------------------------------------------------
If the line k in the xy-plane has equation y=mx +b, where m and b are constants, what is the slope of k?
(1) k is parallel to the line with equation y = (1-m)x+b+1
(2) k intersects the line with equation y = 2x+3 at the point (2,7).
Answer is A. m = 1-m
from 2nd stmt, we cannot get the value of b and m separately.
--------------------------------------------------------------------
Hi.. Can someone please help me answer these questions? Thanks a ton!
Each of the 45 boxes on shelf J weighs less than each of the 44 boxes on Shelf K. What is the median weight of the 89 boxes on these shelves?
(1) The heaviest box on shelf J weighs 15 pounds.
(2) The lightest box on shelf K weighs 20 pounds.
-------------------------------------------------------------------
let d boxes on K b denoted a s k1,k2,k3,k4..... and on shelf J as j1,j2....now j115....so 15 is d median but we cant say so by 2nd statement
cuz its a box n K shelf nothin bt d 45th box is known so answered by 1 only
thnx to sinchan
Answers are (A), (D) and (A) for the 1st, 2nd and 3rd questions respectively..
Thanks a lot for your explanations! =]