What is the remainder when X^4 + Y^4 divide by 5
A) X-Y divided by 5 gives remainder 1
B) X+Y divided by 5 gives remainder 2
i dont have the OA for this
What is the remainder when X^4 + Y^4 divide by 5
A) X-Y divided by 5 gives remainder 1
B) X+Y divided by 5 gives remainder 2
i dont have the OA for this
my approach-
x-y=5p+1
x+y=5q+2
solving for x,y and substituting in x^4+y^4 gives-
x^4=(5(p+q)/2+3/2)
y^4=(5(q-p)+1)^4
the first term of both expressions contains 5 will be cancelled,the remiander will be-
(3/2)^4+1
=97/16
this when divided by 5 will give-(6+1/6)divide by5=6/5+1/30=1
though not sure on the approach but again thought of giving a try.
I guess statement 2 alone is sufficient to answer the question.
Statement 1)try with (11,5 and 7,1) = diff remainders
Statement 2) try with (4,3) and (11,1) and (7,0) = same remainder
What is the remainder when X^4 + Y^4 divide by 5
A) X-Y divided by 5 gives remainder 1
B) X+Y divided by 5 gives remainder 2
i dont have the OA for this
I am very much tempted to believe the Ans should be E
Nothing has been mentioned of x and y being integers, so they can be any real nos
Could not think of mathematical way to conclude...so used nos
St 1 : x= 6 ; y= 5 Rem : 1
x= 2 ; y=1 Rem : 2 ...Hence not suff
St 2 : x=5 ; y=2 Rem : 1
x=4 ; y=3 Rem : 2 ...Hence not suff
P.S : It is not necessary to actually calculate the 4th powers. it is very easy to get the units digit of each using cyclicity rule
Combined : x=1.5 ; y=0.5 Rem : some decimal value
x= 9 ; y=-2 Rem : 2 ...Hence not suff
Ans E ..
Would love to correct my approach if somebody comes up with a clear methodology or concept to do in a shorter time !!
What is the remainder when
X^4 + Y^4 divide by 5
A) X-Y divided by 5 gives remainder 1
B) X+Y divided by 5 gives remainder 2
i dont have the OA for this
from stmt 1
x-y = 5k+1
To find the remainder of X^4+Y^4 we would need remainder of product XY.
so stmt 1 is not sufficient
from stmt 2.
x+y = 5P+2
To find the remainder of X^4+Y^4 we would need remainder of product XY.
so stmt 2 is not sufficient.
From stmt 1 & 2.
x-y = 5k+1
x+y = 5P+2
we get
x = 5k+5p+3
y= 5k-5p+1
remainder of X^4+Y^4 when divided by 5 is remainder , when 3^4 + 1^4 is divided by 5.
so, can be ans using 1&2.
pls correct if im wrong
rgds-
sri
from stmt 1
x-y = 5k+1
To find the remainder of X^4+Y^4 we would need remainder of product XY.
so stmt 1 is not sufficient
from stmt 2.
x+y = 5P+2
To find the remainder of X^4+Y^4 we would need remainder of product XY.
so stmt 2 is not sufficient.
From stmt 1 & 2.
x-y = 5k+1
x+y = 5P+2
we get
x = 5k+5p+3
y= 5k-5p+1
remainder of X^4+Y^4 when divided by 5 is remainder , when 3^4 + 1^4 is divided by 5.
so, can be ans using 1&2.
pls correct if im wrong
rgds-
sri
Sri - 1 doubt : equations u have mentioned are for 2x and 2y resp ..
Hence,
x = (5k+5p+3)/2
y= (5k-5p+1)/2
Now, since (5k+5p)/2 and (5k-5p)/2 may or may not be integers, i dont think we can have fixed remainder ..
Pls correct me if i am wrong ...
Solve this
Jay put 12 cards on a table, some face up and the rest facedown. How many were put facedown?
(A) Jay put an even number of the cards face up.
(B) Jay put twice as many of the cards face up as he put facedown.
A.statement (A) alone is sufficient but statement (B) alone is not
B.statement (B) alone is sufficient but statement (A) alone is not
C.both (A) and (B) together are sufficient but none of them alone is sufficient
D.both statements are sufficient independently
E.both (A) and (B) together are not sufficient
What is the value of X?
(A) When X is multiplied by 8, the result is between 50 and 60.
(B) When X is doubled, the result is between 10 and 15.
Solve this
Jay put 12 cards on a table, some face up and the rest facedown. How many were put facedown?
(A) Jay put an even number of the cards face up.
(B) Jay put twice as many of the cards face up as he put facedown.
A. statement (A) alone is sufficient but statement (B) alone is not
B. statement (B) alone is sufficient but statement (A) alone is not
C. both (A) and (B) together are sufficient but none of them alone is sufficient
D. both statements are sufficient independently
E. both (A) and (B) together are not sufficient
I think the ans is B.
What is the value of X?
(A) When X is multiplied by 8, the result is between 50 and 60.
(B) When X is doubled, the result is between 10 and 15.
IMO E.
Conisder 1) x is not mentioned as an integer so x can be anything
if x= 7 then 7*8 is 56 but if x=6.9 then still the product is still between 50 and 60.
so alone is insuff.
Consider 2) if x=5.5 then 2x=11 if x=7 then 2x = 14
so insuff
consider both still there are many possibilities. SO E
Whats the OA?
What is the value of X?
(A) When X is multiplied by 8, the result is between 50 and 60.
(B) When X is doubled, the result is between 10 and 15.
I'll go with option A
tell me if m wrng
If m right then i'll post the sol bro
Solve this
Jay put 12 cards on a table, some face up and the rest facedown. How many were put facedown?
(A) Jay put an even number of the cards face up.
(B) Jay put twice as many of the cards face up as he put facedown.
A. statement (A) alone is sufficient but statement (B) alone is not
B. statement (B) alone is sufficient but statement (A) alone is not
C. both (A) and (B) together are sufficient but none of them alone is sufficient
D. both statements are sufficient independently
E. both (A) and (B) together are not sufficient
I'll go with option"B"
let me knw if m wrng
Solve this
Jay put 12 cards on a table, some face up and the rest facedown. How many were put facedown?
(A) Jay put an even number of the cards face up.
(B) Jay put twice as many of the cards face up as he put facedown.
Ans B ..
St 2 : 2:1 ratio for a total of 12, hence 4 facedown...
What is the value of X?
(A) When X is multiplied by 8, the result is between 50 and 60.
(B) When X is doubled, the result is between 10 and 15.
Ans E..
X is not necessarily integer ..
St 1 : X is between 50/8 and 60/8 ...not suff
St 2 : X is between 10/2 and 15/2 ...not suff
Combined : still not suff ...
this is option B..
u know the total number of cards and now u also know the ratio in which the cards are placed.. so eqn 2 is suff.. hence B ;)
Solve this
Jay put 12 cards on a table, some face up and the rest facedown. How many were put facedown?
(A) Jay put an even number of the cards face up.
(B) Jay put twice as many of the cards face up as he put facedown.
A. statement (A) alone is sufficient but statement (B) alone is not
B. statement (B) alone is sufficient but statement (A) alone is not
C. both (A) and (B) together are sufficient but none of them alone is sufficient
D. both statements are sufficient independently
E. both (A) and (B) together are not sufficient
What is the value of X?
(A) When X is multiplied by 8, the result is between 50 and 60.
(B) When X is doubled, the result is between 10 and 15.
well.. the value of X can be any real number.. it can be 6.9999, 7.0 or 7.05 or 7.001.. you just cannot reach concrete answer putting the real number values in both eqn A and eqn B..
the answer would be option E
Hi Puys,
Please try the following questions. These are all from previous posts in this thread , but im not convinced by the explanations provided. Please explain ur steps:
1.Lines n and p lie in the xy plane. is the slope of line n less than the slope of line p ?
(1) lines n and p intersect at point (5,1)
(2) the y-intercept of line n is greater than the y-intercept of p
OA: C
2. An integer greater than 1 that is not prime is called composite. If the two digit integer n is greater than 20, is n composite?
1. The tens digit of n is a factor of the units digit of n
2. The tens digit of n is 2
OA: D
3. In the xy plane, what is the y intercept of Line L
1. The slope of line L is 3 times its y intercept
2. the x intercept of line L is -1/3
OA: not available
4.Are x and y both positive?
1) 2x-2y=1
2) x/y >1
OA: C
5. N is a positive three digit number denoted by N=(a^2)*(b), where and b are multiples of 3 and 5. Find N
1. a+b= even number
2.a=b
OA: B
Hi Puys,
Please try the following questions. These are all from previous posts in this thread , but im not convinced by the explanations provided. Please explain ur steps:
1.Lines n and p lie in the xy plane. is the slope of line n less than the slope of line p ?
(1) lines n and p intersect at point (5,1)
(2) the y-intercept of line n is greater than the y-intercept of p
OA: C
The answer is C.
let the equation of line n and p are-y=kx+a and y=px+b
solving these two equations by substituting x,y as 5,1
k-p=(a-b)/5.
a>b from second,
we can conclude k>p.
2. An integer greater than 1 that is not prime is called composite. If the two digit integer n is greater than 20, is n composite?
1. The tens digit of n is a factor of the units digit of n
2. The tens digit of n is 2
OA: D
1. when tens digit is a factor of unit digits-possible numbers:11,13,15,24,26,39,36,48,44 etc.So nothng can be said about the number.
2.when tens is 2, the number can be 21-29.
combining two statements-the nuber has to-24,26,28
so not prime.
C is the answer.
3. In the xy plane, what is the y intercept of Line L
1. The slope of line L is 3 times its y intercept
2. the x intercept of line L is -1/3
OA: not available
let line is y=mx+c.
1.m=3c or c=m/3..not suff
2.x intercept is -c/m=-1/3=>m+3c=0
combining two=>m=0=>y=c
So E
4.Are x and y both positive?
1) 2x-2y=1
2) x/y >1
OA: C
1.x-y=.5=>x,y+ive or x +ive,y-ve or x-ve,y-ve
2.x>y
combining two cant say.
x,y=-2,-2.5 or 2.5,2
E
5. N is a positive three digit number denoted by N=(a^2)*(b), where and b are multiples of 3 and 5. Find N
1. a+b= even number
2.a=b
OA: B
guy with guts
Reg the prblm 55. N is a positive three digit number denoted by N=(a^2)*(b), where and b are multiples of 3 and 5. Find N
1. a+b= even number
2.a=b
OA: B
I feel the ans must be option E since option b can't be achieved for the above conditions and option a is not suff
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.
my answer doesn't match with the OA.. and I am not sure if the OA could be true.. share your thoughts..
(1) The heaviest box on shelf J weighs 15 pounds.
(2) The lightest box on shelf K weighs 20 pounds.
my answer doesn't match with the OA.. and I am not sure if the OA could be true.. share your thoughts..