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Question

A,B and C ran a 100 meters race.They started at the same time and ran at constant speeds throughout . A finished first , B finished second , C finished third. In terms of distance ,by how much distance did A defeated C, when A finished the race?

1) A defeated B by 20 meters.

2) The ratio of speeds of B is to C is 10 is to 7.

1) A defeated B by 20 meters.

2) The ratio of speeds of B is to C is 10 is to 7.

manpreetsingh86 · Answer

st 1: when A covered 100,(i.e. Finishing line) B covered only 80. Since no info about C is provided hence this is not sufficient

st2 : since time is constant. Therefor we have D2=D1(S2/S1)

here D2= distance covered by C
D1 = distance covered by B
S2= speed of C
and S1= speed of B

so when B covered 100 C covered only 70

Also, since no info about A is provided hence this is not sufficient

combining 1 and 2 we know that when A covered 100 B covered 80. So therefore in the same time C will cover
D2 = 80(70/100) = 56 hence distance between A and C = 100-56 =44 hence sufficient.

Therefore correct answer should be C

WoundedTiger · Answer

Sol: We need to know by what distance A beat C.

St 1: A beat B by 20 mts so when A completed 100 mts then B was at 80 meters but we don't know anything about C so. Option A and D ruled out

St 2: Ratio of Speeds is given B:C is 10:7 but we know nothing about A. 
So Option B ruled out

Combining both statements we get that when A =100 mts then B=80 mts and C = 56 mts why??

Cause B:C is 10:7 so (multiply by 8) we get 80:56

Ans is C

innocous · Answer

If p, q, r are positive integers. Is p> q?

1) q> 2r

2)|p-r| > |q-r|

innocous · Answer

A cylindrical tank having a height of h units is filled with water to the maximum capacity of 120 litres. Later on identical holes are drilled at four places along the height at the heights of 0, h/4 , h/2 , 3h/4. If water leaks from the holes at 2litres / min . in how many minutes the tank would be completely empty?

A) 30 MINUTES

B) 30.25 MINUTES

C) 60 MINUTES

D) 45 MINUTES

E) 90 MINUTES

A) 30 MINUTES

B) 30.25 MINUTES

C) 60 MINUTES

D) 45 MINUTES

E) 90 MINUTES

innocous · Answer

How many 5 letter arrangements of alphabets A, B,C,D,E are possible such that alphabets A and B

always come together and alphabet C is never adjacent to either of the alphabets A or B. Repeating

of alphabets is not allowed .

A) 8
B) 16
C) 24
D) 32
E) 64

manpreetsingh86 · Answer

lets consider AB as a one group. then we have  , C, D, E to be arrange.

-,-,-,- lets name these places as 1,2,3,4

Case1 AB comes at position 1 or 4

if   comes at the position 1 then C can occupy either position 3 or 4 and the remaining 2 letters can arrange themselves in 2 ways. Also letters AB can arrange themselves in 2 ways. (AB and BA) Therefore total no. of ways = 1(for AB)*2 (for C)*2(for remaining letters)*2(in which A and B can arrange themselves)
=8
Also, total no. of ways will be same if   comes at the position 4.

Hence total no of ways for case 1 = 8+8 =16

Case 2 AB comes at position 2 or 3

if AB comes at position 2 then C can only occupy position 4, and the remaining two letters can arrange themselves in 2 ways. Also letters AB can arrange themselves in 2 ways (AB and BA). Therefore total no. of ways =1(for AB) *1 (for C) *2(for remaining letters)*2(in which A and B can arrange themselves)
=4

Total no. of ways will be same if   comes at position 3

hence total no. of ways for case 2 = 4+4=8

Total =Case1+Case 2 =16+8 =24

manpreetsingh86 · Answer

st1 is not sufficient as no information is provided about p

st2 it just states that the distance between p and r is greater than distance between q and r. now here two cases are possible

case1 p-------------------q---r
here q is greater than p
case 2 q----r-----------------------------p

here p is greater than q
hence statement 2 alone is not sufficient

combining 1 and 2 we have
q>2r

now for inequality |p-r| > |q-r| to hold true we must have p to be greater than q because the distance between q and r will be greater than r. if p assumes value less than p then the distance between p and r will become less than distance between q and r. which violates the condition statement 2. hence p must be greater than q. therefore answer should be C

manpreetsingh86 · Answer

volume =120, h=0 means hole is at the bottom of the cylinder, 3h/4 results in volume =90, h/2 results in volume =60, h/4 results in volume = 30

initially, volume =120 therefore all of these holes will work simultaneously until volume=90. since rate at which water leaks from these holes =2 therefore all of them when working will leak 8 liters /min. so, it will take  ~4 min.  to leak 30 liters.

Now when volume reaches 90 liters only three holes will work and together they will leak 6 liter/min and it will take them  ~5 min . to leak 30 litre

volume now is 60 liters , therefore only two holes will work at 4 liter/min. Together they will leak 30 liters in  ~8 min

volume left now is 30 liters and at it this instant only bottom hole will work at 2 liter/min and it will empty the cylinder in  15 min.

so therefore total time taken will be 4+5+8+15 = 32

The closest option is B.

MKS · Answer

Stmt 1 - tells about q and r only, can't relate p and q. It means A n D options are out.
Stmt 2 - Modulas implies absolute distance (dist.). Thus 
Dist. between p and r > Dist. btw q and r .
It means numbers will be either in order "p , q, r" or in "r, q, p" on the number line. (note we are also given p,q,r are positive.so don't think about any number being negative)
But this also does not tell which is greater between p and q. Hence B out

Together
St. 2 already restricts to two number orders and then St.1 provides us that q>2r it means q > r always (As given p,q,r are positive)
this restricts the system to number order "r,q,p".
Sufficient . Ans C

MKS · Answer

Notice hole at 3h/4 will not be active once tank has emptied h/4 capacity water i.e. 30 liters, as water will be below that height only
If 4 holes active then total rate = 4*2 = 8 ltr/min
similarly for 3 holes = 6 ltr/min ....

T = 30/8 + 30/6 + 30/4 + 30/2 = (90+120+180+360)/24 = 750/24 = bit more than 30 min. as 750/25= 30 So Ans B

MKS · Answer

Nice questions innocous

Added these to my "Tough questions list"

innocous · Answer

is the slope of line k positive?

1) x-intercept and y-intercept of line k are equal.

2) y-intercept of line k is not equal to zero.

aniketb · Answer

This is how I approached it:
1) Not Sufficient: Lines with negative slope (Lines going like \) have equal intercept, however if intercepts are 0,0 then line with +ve slope (line going like /) will also have same intercepts. hence statement one alone is not sufficient. 
2) Not sufficient :Does not tell anything about X intercept

Combined: Now if both intercepts are equal and Y-intercept is non zero, X-Intercept is non zero too. Hence Line must be of -Ve slope. Sufficient.

IMO C.

Bunuel, Carcass please let us know if above explaination is correct.

dabral · Answer

@aniketb

Your explanation is correct. I just don't think the GMAT likes to play with the x- and y-intercepts being zero, technically they are for a line passing through the origin, but in my experience they tend to avoid that condition, just because it borders on being ambiguous. I haven't seen them play with this in the official GMAT questions. Perhaps others can shed light on this as well.

To keep it in the GMAT spirit, I would modify the question to this:

In the xy-plane, what is the slope of line k that does not pass through the origin?

1) The x-intercept of line k is two more than the y-intercept.

2) The x-intercept of line k is twice the y-intercept.

Cheers,
Dabral

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