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GMAT Prep - DS Geometry
Source: Beat The GMAT — Data Sufficiency |
Concept to remember:in any triangle exterior angle equals to the sum of interior angles. prs=pqr+rpqnaveenhv wrote:Can somebody help me with this?
Stmt 1=> rpq= 30, prs-pqr=30 therefore sufficient.
Stmt 2 => prq+rqp=150, 180- 150=30 (rpq, same with stmt 1) sufficient.
cheers,
Stay skeptical,
Think critically,
Assume nothing.
Think critically,
Assume nothing.
Hey sadullaevd,sadullaevd wrote:Concept to remember:in any triangle exterior angle equals to the sum of interior angles. prs=pqr+rpqnaveenhv wrote:Can somebody help me with this?
Stmt 1=> rpq= 30, prs-pqr=30 therefore sufficient.
Stmt 2 => prq+rqp=150, 180- 150=30 (rpq, same with stmt 1) sufficient.
cheers,
Thanks a lot for the answer.
I am new to this forum. But here is how I would solve the other two questions.
Question #2
Jane's Credit Card Balance -
1. Sufficient. 21st day payment, you can find average balance by
(600*20 + 300*10)/30
2. Sufficient.
Starting balance was $600.
The average balance through 25th day was $540. From this you know that Jane made a payment of 60 dollars in first 25 days. She made the remaining payment of 300-60=240 dollars in next 5 days. You know the average balance for the remaining 5 days would be (545+545+545+545+545 - 240)/5. From two averages, you can find her daily average for the 30 day billing cycle.
Question #3
I think the answer should be C
y=(x+a)(x+b)
If you reduce this equation to y=mx + b format
y=x^2 + xb + xa + ab = x(x+a+b) + ab
The point where line intersects 'x' axis, y=0
so 0 = (x+a)(x+b)
So you know that x=-a or x=-b, when y=0.
1. a+b = -1
Insufficient. reduces first equation to 0 = x(x-1) + ab
Without knowing value of either a or b, you cannot solve.
2. We know that one line on the point is (0,-6)
That means -6=0 (0+a+b)+ab
so you can ab=-6
You already know that x=-a or x=-b but ab=-6 does not solve the problem. So insufficient.
Now combining them together you have ab=-6 and a+b=-1 From this you can find values of a and b. Input them in the first equation and solve the equation for x but inputting value of 'y' as 0.
So answer should be C.
Question #2
Jane's Credit Card Balance -
1. Sufficient. 21st day payment, you can find average balance by
(600*20 + 300*10)/30
2. Sufficient.
Starting balance was $600.
The average balance through 25th day was $540. From this you know that Jane made a payment of 60 dollars in first 25 days. She made the remaining payment of 300-60=240 dollars in next 5 days. You know the average balance for the remaining 5 days would be (545+545+545+545+545 - 240)/5. From two averages, you can find her daily average for the 30 day billing cycle.
Question #3
I think the answer should be C
y=(x+a)(x+b)
If you reduce this equation to y=mx + b format
y=x^2 + xb + xa + ab = x(x+a+b) + ab
The point where line intersects 'x' axis, y=0
so 0 = (x+a)(x+b)
So you know that x=-a or x=-b, when y=0.
1. a+b = -1
Insufficient. reduces first equation to 0 = x(x-1) + ab
Without knowing value of either a or b, you cannot solve.
2. We know that one line on the point is (0,-6)
That means -6=0 (0+a+b)+ab
so you can ab=-6
You already know that x=-a or x=-b but ab=-6 does not solve the problem. So insufficient.
Now combining them together you have ab=-6 and a+b=-1 From this you can find values of a and b. Input them in the first equation and solve the equation for x but inputting value of 'y' as 0.
So answer should be C.
The last question of the series. I got this question right. But i wan to know the exact reason this is right.
Question 1.
1. Insufficient.
2. Insufficient.
Combined - visualize it this way
TB1________TB2_______TB3______TB4
Now the distance between TB1 and TB4 is 25.
There are three intervals between Those two. If all three intervals were 10 or more the distance between TB1 and TB4 should have been 30 or more. But it is less than 30. So there must be at least one pair of toll booths that are less than 10 miles apart.
The answer is C.
Question 2:
We know there were 15,000 books purchased.
1. gives us M+F = 4000 Insufficient.
2. gives us 3M + 5F = 15000. Insufficient.
But, together You can solve the above equation and find 'F'. So answer is C.
1. Insufficient.
2. Insufficient.
Combined - visualize it this way
TB1________TB2_______TB3______TB4
Now the distance between TB1 and TB4 is 25.
There are three intervals between Those two. If all three intervals were 10 or more the distance between TB1 and TB4 should have been 30 or more. But it is less than 30. So there must be at least one pair of toll booths that are less than 10 miles apart.
The answer is C.
Question 2:
We know there were 15,000 books purchased.
1. gives us M+F = 4000 Insufficient.
2. gives us 3M + 5F = 15000. Insufficient.
But, together You can solve the above equation and find 'F'. So answer is C.
Last question
we know that distance between x and y is greater than distance between x and z.
1. xyz<0
That means either all three are less than 0 or only 1 of them is less than 0.
x=-2, y=-4 and z=-1 shows that z is not in between x and y.
x=2, y=-4 and z=1 shows that z is in between.
So it is insufficient.
2. xy<0
This tells you either x or y is less than 0 and the other is positive.
x=2, y=-4 and z=1 shows that z is in between.
x=-2 y =4 and z=-1 shows that z is not in between. Insufficient.
Now putting them together we know this much that
z is positive
if x is positive, y is negative
x=2, y=-4, z=1 shows that z is in between
x=2, y=-4, z=3 shows that z is not inbetween
We don't even need to know the scenario where y is positive and x is negative. Because we don't know for sure if that is the case.
So the answer should be E.
we know that distance between x and y is greater than distance between x and z.
1. xyz<0
That means either all three are less than 0 or only 1 of them is less than 0.
x=-2, y=-4 and z=-1 shows that z is not in between x and y.
x=2, y=-4 and z=1 shows that z is in between.
So it is insufficient.
2. xy<0
This tells you either x or y is less than 0 and the other is positive.
x=2, y=-4 and z=1 shows that z is in between.
x=-2 y =4 and z=-1 shows that z is not in between. Insufficient.
Now putting them together we know this much that
z is positive
if x is positive, y is negative
x=2, y=-4, z=1 shows that z is in between
x=2, y=-4, z=3 shows that z is not inbetween
We don't even need to know the scenario where y is positive and x is negative. Because we don't know for sure if that is the case.
So the answer should be E.
Take a look at link belownaveenhv wrote:Another one:
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https://www.beatthegmat.com/gmatprep-pra ... t8293.html
Stuart has great exp.
cheers,
Stay skeptical,
Think critically,
Assume nothing.
Think critically,
Assume nothing.
x=-2 y =4 and z=-1 shows that z is not in between. Insufficient.superdesi2100 wrote:Last question
we know that distance between x and y is greater than distance between x and z.
1. xyz<0
That means either all three are less than 0 or only 1 of them is less than 0.
x=-2, y=-4 and z=-1 shows that z is not in between x and y.
x=2, y=-4 and z=1 shows that z is in between.
So it is insufficient.
2. xy<0
This tells you either x or y is less than 0 and the other is positive.
x=2, y=-4 and z=1 shows that z is in between.
x=-2 y =4 and z=-1 shows that z is not in between. Insufficient.
Now putting them together we know this much that
z is positive
if x is positive, y is negative
x=2, y=-4, z=1 shows that z is in between
x=2, y=-4, z=3 shows that z is not inbetween
We don't even need to know the scenario where y is positive and x is negative. Because we don't know for sure if that is the case.
So the answer should be E.
isnt z between x and y? -2----(-1)-----4, I guess instead of (-1), its better to plug (-3) which is really not between x and y.
correct me, if im wrong.
cheers,
Stay skeptical,
Think critically,
Assume nothing.
Think critically,
Assume nothing.
Yes, you are right.sadullaevd wrote:
x=-2 y =4 and z=-1 shows that z is not in between. Insufficient.
isnt z between x and y? -2----(-1)-----4, I guess instead of (-1), its better to plug (-3) which is really not between x and y.
correct me, if im wrong.
cheers,
