In this case, P can be equal to = 32,33,34,35,36 None of them is a prime number, so yes Positive integer P be expressed as the product of 2 integers, Each of which is greater than 1.
Statement I sufficient. 2. P is Odd Well except 2, all prime numbers are odd, so P can be something like 5,7,17. In that case P cannot be expressed as the product of 2 integers
Statement II, insufficient.
Combining 2 statement P can be equal to =33,35 In both case can be expressed as the product of 2 integers. So Together also sufficient.
Why do we need to combine the two statements when 1 is sufficient and 2 is not? It will correspond to Option A. of the DS type questions on GMAT.
Yesterday Nan parked her car at a certain parking garage that charges more for the first hour than for each additional hour. If Nans total parking charge at the garage yesterday was $3.75, for how many hours of parking was she charged?
(1) Parking charges at the garage are $0.75 for the first hour and $0.50 for each additional hour or fraction of an hour. (2) If the charge for the first hour had been $1.00, Nans total parking charge would have been $4.00.
Yesterday Nan parked her car at a certain parking garage that charges more for the first hour than for each additional hour. If Nans total parking charge at the garage yesterday was $3.75, for how many hours of parking was she charged?
(1) Parking charges at the garage are $0.75 for the first hour and $0.50 for each additional hour or fraction of an hour. (2) If the charge for the first hour had been $1.00, Nans total parking charge would have been $4.00.
We cant answer even by combining both as we donot know whether its 7 hrs or 6 hr and some mins. . .
Yesterday Nan parked her car at a certain parking garage that charges more for the first hour than for each additional hour. If Nan's total parking charge at the garage yesterday was $3.75, for how many hours of parking was she charged?
(1) Parking charges at the garage are $0.75 for the first hour and $0.50 for each additional hour or fraction of an hour. (2) If the charge for the first hour had been $1.00, Nan's total parking charge would have been $4.00.
My take:
Opt I. Charges for first hour = 0.75$ Total charge = 3.75$ ==> charge for remaining hours = $3.00 rate for each additional hour/fraction hour = $ 0.50 Question doesnt ask how many hours was she parked rather it asks how many hours of parking she was charged. So
1 hr + (3.00/0.5) = 7 hrs. Option I is sufficient.
Opt II. If parking charge for 1st hr = $ 1.00, remainder charge = 4.00 -1 = $ 3.00. However without the information of the parking charge rate it's not possible to calculate the number of hours of parking charge. Hence II is insufficient. Ans: A.
OPT I and OPT II : only one pair out of {r,t}= {-12,-6,-2,-4,-3,-1,1,2,3,4,6,12} satisfies the equality{r,t}={3,4}: rt=12 , r+t=7. Hence it is determined that r> 0
Q2)If m is a positive integer, then m*m*m(m-cubed) has how many digits? (1)m has 3 digits (2)m*m has 5 digits
Solution:
OPT I: m has 3 dig ==> m = {100,999} ==> m(cube) = {1000000(7 digits), 997002999(9 digit) } Hence m(cube) varies between 7 digits to 9 digits. NOT Sufficient.
OPT II :m*m has 5 digits ==> m*m = {10000, 99999} ==> m = {100, 316} ==> m*m*m = {1000000(7 digits) , 31554496(8 digits)} Hence m(cube) varies between 7 digits and 8 digits. NOT Sufficient
OPT I and OPT II : m = {100, 316} is a subset of m = {100,900} . Hence both options are NOT Sufficient. Ans: E.
Note: This problem does involve some approximations. WE dont need to actually calulate 999(cube), just an approximation of number of digits is sufficent.
Come __ON PG>>>>SSSS.....Guys One more please answer this
If set S consists of the numbers 1, 5, -2, 8, and n, is 0 (1) The median of the numbers in S is less than 5. (2) The median of the numbers in S is greater than 1.
Come __ON PG>>>>SSSS.....Guys One more please answer this If set S consists of the numbers 1, 5, -2, 8, and n, is 0 (1) The median of the numbers in S is less than 5. (2) The median of the numbers in S is greater than 1.
Solution:
OPT I: if median n ={...-2,-1,0,1,2,3,4}. thus inSufficient.
OPT II: if median > 1 ==> n={2,3,4...}. thus insufficient.
Taking both options together n={2,3,4} ==> 0Sufficient. Ans: C
Come __ON PG>>>>SSSS.....Guys One more please answer this If set S consists of the numbers 1, 5, -2, 8, and n, is 0 (1) The median of the numbers in S is less than 5. (2) The median of the numbers in S is greater than 1.
2)B--second statement alone is enough... 1/k+1>0 =>1/k>-1 =>kThus, 1/kHowever, the first statement gives us k
Slight error in Q no. 2 plz forgive Actually, statement 1 can also give us the answer 1/k-1>1 =>1/k>2 Thus, 1/k>0. So, the answer should be C...either statement alone is enough
As for Q no. 1, equation of the line is y= -x/10 +c, where c>1....(slope-intercept form)..using both the data =>10y +x= 10c, c>1 While the equation of the circle is x^2+ y^2 = 1 If the two equations can be solved, it means the line intersects the circle; if they cannot be solved, line does not intersect. But we cannot say if the equations have a solution, until the value of c is determined. Given data is insufficient. So, E.
Slight error in Q no. 2 plz forgive Actually, statement 1 can also give us the answer 1/k-1>1 =>1/k>2 Thus, 1/k>0. So, the answer should be C...either statement alone is enough
As for Q no. 1, equation of the line is y= -x/10 +c, where c>1....(slope-intercept form)..using both the data =>10y +x= 10c, c>1 While the equation of the circle is x^2+ y^2 = 1 If the two equations can be solved, it means the line intersects the circle; if they cannot be solved, line does not intersect. But we cannot say if the equations have a solution, until the value of c is determined. Given data is insufficient. So, E.
Crab Bro, m sorry but i think for the second question 2) K Not equal To 0,1 & -1 IS 1/K>0
a 1/k-1>1 b 1/k+1>0
only, A is the ans....B is wrong....explanation 1/k+1>0 => 1/k > -1 => -1 1/k can also be -1/2, -1/3 and can be ny positive no...as 1/k can be greater or lesser than zero so op B is not definate hence only A is the rite ans...
Slight error in Q no. 2 plz forgive Actually, statement 1 can also give us the answer 1/k-1>1 =>1/k>2 Thus, 1/k>0. So, the answer should be C...either statement alone is enough
As for Q no. 1, equation of the line is y= -x/10 +c, where c>1....(slope-intercept form)..using both the data =>10y +x= 10c, c>1 While the equation of the circle is x^2+ y^2 = 1 If the two equations can be solved, it means the line intersects the circle; if they cannot be solved, line does not intersect. But we cannot say if the equations have a solution, until the value of c is determined. Given data is insufficient. So, E.
Crab Bro, m sorry but i think for the second question 2) K Not equal To 0,1 & -1 IS 1/K>0
a 1/k-1>1 b 1/k+1>0
only, A is the ans....B is wrong....explanation 1/k+1>0 => 1/k > -1 => -1 1/k can also be -1/2, -1/3 and can be ny positive no...as 1/k can be greater or lesser than zero so op B is not definate hence only A is the rite ans...
1. Is n/18 an integer? (1) 5n/18 is an integer. (2) 3n/18 is an integer.
ANs: A 1. 5n/18 is an intgr ==> n is perfectly divisible by 18 because 18 and 5 have no common factors or are co-prime numbers. Hence Opt 1 alone is sufficient.
2. 3n/18 is an intgr ==> 3 is the common factor between 3 and 18 so we cannot be certain if n is completely divisible by 18. SO Opt 2 alone is insufficient.
If ab is not equal to 0, and points (-a,b) and (-b,a) are in the same quadrant of the xy plane, is point (-x,y) in this same quadrant? (1) xy>0 (2) ax>0