1. Is the measure of one of the interior angles of quadrilateral ABCD equal to 60 degrees? (1)Two of the interior angles of ABCD are right angles. (2)The degree measure of angle ABC is twice the degree measure of angle BCD. 2. If K is a positive integer, is K the square of an integer? (1)K is divisible by 4 (2)K is divisible by exactly 4 different prime numbers 3. Is x (1) The ratio of x to y is 7/9 (2) xy>0 4. What is the median number of employees assigned per project for the projects at Company Z? (1)25 percent of the projects at Company Z have 4 or more employees assigned to each project. (2)35 percent of the projects at Company Z have 2 or fewer employees assigned to each project.
1. At first, I thought the answer for this will be C as I thought that combining both of them, we can reach that none of the angles will be 60 degrees.
But after solving the 2nd problem, I retrospect that there will be one condition when option 1 and 2 can't survive with each other and thats why the anwer will be E.
@Italian - What was your logic for E ?
2. Option 1: k is divisible by 4. K can be 4 or 20 so it can or can not be square of an integer. Not sufficient. Option 2 : K is divisible by exactly 4 different prime numbers. consider k = 210 = 2 x 3 x 5 x 7. But its not square of an integer whereas if K = 210^2 it will be. Not sufficient. option 1 and 2 : Can not co-exist. Not sufficient.
Answer will be E.
3. Is x Option 1: x/y = 7/9. If x and y are positive, x 0. Same logic as above. Not suffficient. Option 1 abd 2: Again not sufficient.
Answer should be E.
4. if you'll consider both the options simultaneously, the median will be 3.
Using (1) we can say the line segment lies on the line. Using (2) - we cant sya - it depends on the y-intercept.
coming to your question... two parallel lines cannot overlap each other... if they overlap they are called coincident lines..
The ans shud be D
From stem 1: y = -x+4..slope is -1; hence line is parallel to QR and can never intersect it. We need not even calculate eqn of QR; the fact that slope of line S and of segment QR is same implies that the two are parallel to each other.
Statement 2: we know the slope of line S = -1; hence it can never intersect segment QR
From stem 1: y = -x+4..slope is -1; hence line is parallel to QR and can never intersect it. We need not even calculate eqn of QR; the fact that slope of line S and of segment QR is same implies that the two are parallel to each other.
Statement 2: we know the slope of line S = -1; hence it can never intersect segment QR
wats the OA?
thanks
Q3 is quite straight forward
Stem 1: x/y = 7/9 => x = 7a, y = 9a, where a is some constant take a = 1/7 => x = 1 and y = 9/7 (x x=-1 and y = -9/7 (x>y)
Stem 2: For above values of x and y, xy >0 as both x and y can take the same sign at any given point of time
Combining both nothing can be concluded. Hence E
Q1) Stem 1: Two of the angles are 90 deg but we do not knw abt other two, hence insuff Stem 2: Two angles are such that one is twice the other......still insuff
Combining 1 & 2 => Two angles re 90 deg each so obviously statement 2 refers to other 2 angles x+2x+180 = 360, and x can be solved for Hence C
@ Dopa and Italian: Wats ur logic behind E?
Now coming to Q3) The ques is a yes/no type If there is no ay when statements 1 & 2 can co-exist simultaneously, then answer is a NO which still answers the ques
hence my take is C
@ Dopa again and all junta, correct me if I'm wrong or my logic is flawed.
1. At first, I thought the answer for this will be C as I thought that combining both of them, we can reach that none of the angles will be 60 degrees.
But after solving the 2nd problem, I retrospect that there will be one condition when option 1 and 2 can't survive with each other and thats why the anwer will be E.
@Italian - What was your logic for E ?
2. Option 1: k is divisible by 4. K can be 4 or 20 so it can or can not be square of an integer. Not sufficient. Option 2 : K is divisible by exactly 4 different prime numbers. consider k = 210 = 2 x 3 x 5 x 7. But its not square of an integer whereas if K = 210^2 it will be. Not sufficient. option 1 and 2 : Can not co-exist. Not sufficient.
Answer will be E.
3. Is x Option 1: x/y = 7/9. If x and y are positive, x 0. Same logic as above. Not suffficient. Option 1 abd 2: Again not sufficient.
Answer should be E.
4. if you'll consider both the options simultaneously, the median will be 3.
Answer should be C.
in Q2...the stat 2 states that the number is exactly divisible by 4 prime nos. So if u consider 210, it is not a square of any number, but when u consider 210^2, u dont take consider the "only 4 prime nos." can u elaborate or correct me.....
Quote: Originally Posted by Inder.14 View Post Does line S intersect line segment QR? (1) The equation of line S is y = -x + 4. (2) The slope of line S is -1. the figure is attached for reference my only concern here is can two parallel lines overlap each other like if i say there is a line segment PQ can we draw a line AB parallel to PQ and passing through points P and Q
My take 'A'.
Using (1) we can say the line segment lies on the line. Using (2) - we cant sya - it depends on the y-intercept.
coming to your question... two parallel lines cannot overlap each other... if they overlap they are called coincident lines..
The ans shud be D
From stem 1: y = -x+4..slope is -1; hence line is parallel to QR and can never intersect it. We need not even calculate eqn of QR; the fact that slope of line S and of segment QR is same implies that the two are parallel to each other.
Statement 2: we know the slope of line S = -1; hence it can never intersect segment QR
wats the OA?
thanks
hi alchemist-mba and srikanth267...
the answer given is A the explanation given was Line S has the same slope as line segment QR, so they are parallel. They might intersect; for example, if Line S passes through points Q and R. But they might never intersect; for example, if Line S passes above or below line segment QR. but i totally disagree with the explanation.............can someone who think it is right explain it in detail
Quote: Originally Posted by Inder.14 View Post Does line S intersect line segment QR? (1) The equation of line S is y = -x + 4. (2) The slope of line S is -1. the figure is attached for reference my only concern here is can two parallel lines overlap each other like if i say there is a line segment PQ can we draw a line AB parallel to PQ and passing through points P and Q
My take 'A'.
Using (1) we can say the line segment lies on the line. Using (2) - we cant sya - it depends on the y-intercept.
coming to your question... two parallel lines cannot overlap each other... if they overlap they are called coincident lines..
hi alchemist-mba and srikanth267...
the answer given is A the explanation given was Line S has the same slope as line segment QR, so they are parallel. They might intersect; for example, if Line S passes through points Q and R. But they might never intersect; for example, if Line S passes above or below line segment QR. but i totally disagree with the explanation.............can someone who think it is right explain it in detail
Hi,
The equation of line passing those two points is y = -x+4.
Stmt 1- The equation of line S is y = -x + 4. => both these lines are coincident lines hence.. they intersect each other.=> sufficient.
Stmt 2- The slope of line S is -1. Equation would be y = -x + C... if C =4.. then the line is coincident, means.. they intersect. if C is not 4.. => They are Parallel lines.. wont intersect...
my only concern here is can two parallel lines overlap each other
like if i say there is a line segment PQ can we draw a line AB parallel to PQ and passing through points P and Q
my pick is D..
s1 : when y = (-1) x + 4, it has to pass through the points (1,3) (2,2) which means line S passes through or coincides with the line segment but does not "intersect" s2: s = -1 can be parallel to the line segment as its slope is as well -1. so it cant intersect at any point.
The surface area of a square tabletop was changed so that one of the dimensions was reduced by 1 inch and the other dimension was increased by 2 inches. What was the surface area before these changes were made? (1) After the changes were made, the surface area was 70 square inches. (2) There was a 25 percent increase in one of the dimensions
Seems pretty simple to me. But I got the wrong answer !
The surface area of a square tabletop was changed so that one of the dimensions was reduced by 1 inch and the other dimension was increased by 2 inches. What was the surface area before these changes were made? (1) After the changes were made, the surface area was 70 square inches. (2) There was a 25 percent increase in one of the dimensions
Seems pretty simple to me. But I got the wrong answer !
My take 'D'....
let 'x' be the square side. one of the dimensions was reduced by 1 inch and the other dimension was increased by 2 inches.... area now is: (x-1) (x+2)
stmt 1 --- After the changes were made, the surface area was 70 square inches.. => (x-1) (x+2) = 70. => x = -9 or 8 => sufficient
stmt 1 --- There was a 25 percent increase in one of the dimensions => x is now (x+2) => this is given as 25% increase.. => x = 8 => sufficient.
1. At first, I thought the answer for this will be C as I thought that combining both of them, we can reach that none of the angles will be 60 degrees.
But after solving the 2nd problem, I retrospect that there will be one condition when option 1 and 2 can't survive with each other and thats why the anwer will be E.
@Italian - What was your logic for E ?
2. Option 1: k is divisible by 4. K can be 4 or 20 so it can or can not be square of an integer. Not sufficient. Option 2 : K is divisible by exactly 4 different prime numbers. consider k = 210 = 2 x 3 x 5 x 7. But its not square of an integer whereas if K = 210^2 it will be. Not sufficient. option 1 and 2 : Can not co-exist. Not sufficient.
Answer will be E.
3. Is x Option 1: x/y = 7/9. If x and y are positive, x 0. Same logic as above. Not suffficient. Option 1 abd 2: Again not sufficient.
Answer should be E.
4. if you'll consider both the options simultaneously, the median will be 3.
Answer should be C.
Dopa,
for Q3, the question is is x x/y from A)x/y=7/9 =>sufficient from B)xy>0 => not sufficient
1- frm stem 1 -- we can say x+y+90+90 = 360 , x+y=180 (not sufficient) frm stem 2 -- y = 2x (not sufficient) combine both, x+y =180 , substitute frm stem2, x+2x=180, 3x=180, x=60
(pls correct me if i hav missed something)
2. E s1 - many digits div by 4 are not squares, eg.,8,12 s2 - prd by the 4 distinct prime numbers, 210..or any other prd doesnt appear to be square
3. s1 - consider for -ve values of x and y. (insufficient) s2 - not sufficient. xy>0 can give many options
4. 25 pc of the company >= 4 35 pc of the comp remaining 40% should be inbetween which is 3 combining both, we cud find the median
Thnx for the explanation...For Q4 it was really helpful.... I have a small doubt regarding Q2.....as u xplained..the St 2 answers the ques...so the choice should be 'b' instead of 'e'. correct me if m goin wrong...
Q1. if X>1 and Y>1, is X (1) X^2/(XY+X) (2) XY/Y^2-Y
Q2. If x^3y^4=5,000, is y=5? (1)y is a positive integer. (2)x is an integer. Q3. A certain carton holds fewer than 50 books. What is the number of books in the carton? (1) The books in the carton can be divided into 3 stacks of X books each, with 2 books left over. (2) The books in the carton can be divided into Y stacks of 7 books each, with 2 books left over. Q4. Does the decimal equivalent of P/Q, where P and Q are positive integers, contain only a finite number of nonzero digits? (1) P>Q (2) Q=8 Q5. During a 10-week summer vacation, was the average (arithmetic mean) number of books that Carolyn read per week greater than the average number of books that Jacob read per week? (1) Twice the average number of books that Carolyn read per week was greater than 5 less than twice the average number of books that Jacob read per week. (2) During the last 5 weeks of the vacation, Carolyn read a total of 3 books more than Jacob. Q6. in a certain game played with red chips and blue chips, each red chip has a point value of X and each blue chip has a point value of Y, where X>Y and X and Y are positive integers. If a player has 5 red chips and 3 blue chips, what is the average (arithmetic mean ) point value of the 8 chips that the player has? (1) The average point value of one red chip and one blue chip is 5. (2) The average point value of the 8 chips that the player has is an integer.
Sorry for overloading the ques but here are few more
Q1. If x and y are integers and x > 0, is y > 0? (1) 7x 2y > 0 (2) -y Q2. In the sequence of nonzero numbers t1, t2, t3, , tn, , tn+1 = tn / 2 for all positive integers n. What is the value of t5? (1) t3 = 1/4 (2) t1 - t5 = 15/16 Q3. Is y x positive? (1) y > 0 (2) x = 1 - y
