GMAT Data Sufficiency Discussions

MBA GMAT
2573
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



Ans: C.

xy > 0 ==> (-x,y) in IInd or IVth quad.

ax>0 ==> (-x,y) in Ist, IInd, IIIrd or IVth quad.

taking both it is certain that (-x,y) will be in same quadrant which (-a,b) is in, hence both options are sufficient.
2574
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

My ans is op A

given that,
ab not equal 0,and
(-a,b) and (-b,a) lie in same quadrant----->before solving the question, check the validity of this given condition..it is valid only in two cases..
a>0, b>0, (-a,b) and (-b,a) lie in same quad...2nd quad
ain cases a>o,b0...(-a,b) and (-b,a) doesnt lie in same quad hence invalid

now...Op A...xy>0 => x>0, y>0 or xin 1st case (-x,y) lie in 2nd quad VALID
in 2nd case (-x,y) lie in 4th quad VALID
SO OPA SUFFICIENT

OP B...no info of y...so y can be anything and so quad of (-x,y) may
vary...

Hence OP A is correct

Wats the OA????
2575
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.

Ans is C buddy...its a tough one
1. Is n/18 an integer? (1) 5n/18 is an integer. (2) 3n/18 is an integer.
(1) INSUFFICIENT: We are told that 5n/18 is an integer.
means n= 18, 36,...also n can be= 18/5, 36/5,....because n=int is not given so n can be fractional and in this case
if n=18/5 then n/18= 1/5 which is not an integer.but .for n=18, n/18=int
Hence not sufficient...

(2) INSUFFICIENT: u already know...

(1) AND (2) SUFFICIENT: If 5n/18 and 3n/18 are both integers,
the difference of 5n/18 and 3n/18 will also be integer as, (integer - integer = integer)
So 5n/18 - 3n/18 = 2n/18 = n/9 = integern is a multiple of 9 So n is a multiple of both 6 and 9 so n is a multiple of 18.

the correct answer is C
2576
My ans is op A

given that,
ab not equal 0,and
(-a,b) and (-b,a) lie in same quadrant----->before solving the question, check the validity of this given condition..it is valid only in two cases..
a>0, b>0, (-a,b) and (-b,a) lie in same quad...2nd quad
ain cases a>o,b0...(-a,b) and (-b,a) doesnt lie in same quad hence invalid

now...Op A...xy>0 => x>0, y>0 or xin 1st case (-x,y) lie in 2nd quad VALID
in 2nd case (-x,y) lie in 4th quad VALID
SO OPA SUFFICIENT

OP B...no info of y...so y can be anything and so quad of (-x,y) may
vary...

Hence OP A is correct

Wats the OA????



What abt the condition if (-x,y) lie in the 2nd quadrant and (-a,b) in the IVth quad?

lets say {a,b} = 4,6
and {x,y} = 2,3

thus {-a,b} and {-x,y} both lie in the IInd quad. Hence valid

but {a,b} = -4,-6
and {x,y} = 2,3

then {-a,b} is in IVth quad and {-x,y} is in IInd quad. Option a doesnt give this information, the relation between a and x which is given by option b.
2577
Ans is C buddy...its a tough one
1. Is n/18 an integer? (1) 5n/18 is an integer. (2) 3n/18 is an integer.
(1) INSUFFICIENT: We are told that 5n/18 is an integer.
means n= 18, 36,...also n can be= 18/5, 36/5,....because n=int is not given so n can be fractional


Excellent problem. Missed the crucial fact that n is not mentioned as an integer ..
2578
Switr Says
Excellent problem. Missed the crucial fact that n is not mentioned as an integer ..

yeah buddy...
2579
What abt the condition if (-x,y) lie in the 2nd quadrant and (-a,b) in the IVth quad?

lets say {a,b} = 4,6
and {x,y} = 2,3

thus {-a,b} and {-x,y} both lie in the IInd quad. Hence valid

but {a,b} = -4,-6
and {x,y} = 2,3

then {-a,b} is in IVth quad and {-x,y} is in IInd quad. Option a doesnt give this information, the relation between a and x which is given by option b.

Thanks for the correction bro...
The info. of B is important for a definite solution...
ans is C
2580
Math (DS)

On the picture above, is the area of the triangle greater than 1?

1.
2. Perimeter of the triangle is greater than
2581

Is X divisible by 15?

1. When X is divided by 10, the result is an integer
2. X^2 is a multiple of 30

2582
Is X divisible by 15?

1. When X is divided by 10, the result is an integer
2. X^2 is a multiple of 30



Statement 1 alone is not sufficient (take x =20)
Statement 2 alone is also not sufficient (take x = under root 30, dont know how to put in sign)

Taking both statements together thn x is a multiple of 10 and its also power of 5*3*2 n hence also divisible by 15.

My Ans (C)
2583

Originally Posted by atulmangal

"a>0, b>0, (-a,b) and (-b,a) lie in same quad...2nd quad
a"

Pls elaborate the same via any example.
thnks in adv.

2584
Is X divisible by 15?

1. When X is divided by 10, the result is an integer
2. X^2 is a multiple of 30



My take:

Opt I: X= 10k. Not sufficient to answer if X%15 = 0.

OPT II: X*X = 5*3*2*m ==> X uniquely has all the prime factors {2,3,5} since squaring numbers automatically squares it's factors too. Sufficient.

Ans: B
2585
My take:

Opt I: X= 10k. Not sufficient to answer if X%15 = 0.

OPT II: X*X = 5*3*2*m ==> X uniquely has all the prime factors {2,3,5} since squaring numbers automatically squares it's factors too. Sufficient.

Ans: B



Wht if x = root 30, dear.
2586
dcprinceicai Says
Wht if x = root 30, dear.


Yes, sqrt(30) is a valid option for X hence option B alone doesnt stand. i overlooked that in my analysis. Thanks.
2587

C, both together suffice

Is X divisible by 15?

1. When X is divided by 10, the result is an integer
2. X^2 is a multiple of 30
2588

My take, E, cannot be determined.

Math (DS)

On the picture above, is the area of the triangle greater than 1?

1.
2. Perimeter of the triangle is greater than
2589
Originally Posted by atulmangal

"a>0, b>0, (-a,b) and (-b,a) lie in same quad...2nd quad
a"

Pls elaborate the same via any example.
thnks in adv.

1st case, a>0, b>0, let a=1, b=2
so, (-a,b) = (-1,2)---sketch it in the X-Y plane, it lies in 2nd quad
and (-b,a) = (-2,1)...again...sketch it...it lies in 2nd quad...

it means, for a>0, b>0, for any +ve value of a,b.....(-a,b) and (-b,a) lie in same quad...i.e 2nd quad

2nd case aso, (-a,b) = (1,-2)----->---sketch it in the X-Y plane, it lies in 4th quad
and (-b,a) = (2,-1)...again...sketch it...it lies in 4th quad..

it means, for a
The same quad thing doesnt appear if u reverses the signs of a,b i.e a>0,b0
for ex...for a>0,b(-a,b) = (-1,-2)----lies in 3rd quad
(-b,a) = (2,1)------lies in 1st quad
hence in this scenario both points doesnt lie in same quad

Hope now its clear
2590
sausi007 Says
My take, E, cannot be determined.


Pls also provide the approach you've taken to solve the problem.

My take: I : ABC not sure on the relevance of this info :shocked:...

II: finally i get the relation ax > 1 where a = area of ABC
x = one of the equal sides of the isosceles triangle.

now from the figure, x = sqrt(a^4 + 1/a^2)
since ax > 1 ==> a>0, x>0
plugging in values: a = 0.5 , x = sqrt(0.0625 + 4) = 2.01 ~ 2
with x = 2, and 2/a = 4 we get perimeter = 8.
with a = 1.5, x=sqrt(5.0625+1/)=2.34. thus perimeter= 2.35 +2.35 + 1.333 = 6.03 > 2.667
with a = 0.2, x=sqrt(0.0016 + 25) = 5
thus peri = 5+5+0.4 =10.4
Hence the above holds only when a>1. Thus info in B is sufficient to conclude that a>1 ==> A(ABC) > 1.

ANS: B
NOTE: just checked for a=0.9, the relation holds, so i guess it's E now :)
2591

Is 4Q/11 a positive integer?
1. Q is a prime number
2. 2Qis divisible by 11

2592

A for me.

Area of triangle = 1/2 * 2/a * a^2 = a. Hence, we need to find out whether a > 1/

From stmt1: AB^2 + BC^2 > AC^2 or 2*AB^2 > AC^2
or 2*(a^4 + 1/a^2) > 4/a^2
or, (a^6 + 1) > 2 or, a^6 > 1 that means a > 1. Hence, sufficient.

(a could be -2 also but since since a is a measurement of length of sides, a cannot be -ve. therefore a has some +ve value.)



Simplifying stmt2 will give a > 0...insufficient.
Perimeter = AB + BC + AC = 2AB + AC = 2*sqrt((1/a^2)+ a^4) + 2/a
= 2*(sqrt(1+a^6))/a + 2/a > 4/a
or, sqrt(1+a^6) + 1 > 2
or, sqrt(1+a^6) > 1 or a > 0.

Hope it clears the air.