GMAT Problem Solving Discussions

MBA
281
answer is e .. coz irrespective of the length of the strip we can always find a square tile inside satisfying the given ratio
should not the question be least possbl integer that mst divide n ?
lcm of all the numbers 2520


Even i thought the 2nd ques shld be "least" and not "largest"
282
Hey guys,

can u help me out with these??

1) A square countertop has a square tile inlay in the cente, leaving an untiled stripof uniform width around the tile. If the ratio of the tiled area to the untiled area is 25 to 39, which of the following could be the width in inches of the strip?

a) 1.5
b) 3
c) 4.5

a) a only
b) b only
c) a and b only
d) a and c only
e) a, b and c

2) If n is a positive integer and n^2 is divisible by 72, then the largest possible integer that must divide n is

a) 6
b) 12
c) 24
d) 36
e) 48

3) Whcih of the following is the least positive integer that is divisible by 2,3,4,5,6,7,8,9 ?

a) 15120
b) 3024
c) 2520
d) 1890
e) 1680

Could you post your ans with the explns??


1) if a is the side of the square and let b be the width

ares of square = a^2 = 25
of outer one = (a+2b)^2 = 25+39 = 64

so as ratio is given if a= 5 b =1.5
a= 10 b = 3
a=15 b= 4.5


2) 72 = 2^3*3^2

so n should have 2^2 and 3

so largest possible integer that must divide n is 12 (its largest see the word must)

3) we have 5 7 8 and 9 which will cover all

so 63 *40 = 2520
283

Guys,

Is it always true that in a right angled triangle inscribed in a circle, the hypotenuse is always the diameter??

Is it possible to construct a right-triangle inscribed in a circle, where the hypotenuse is not the diameter??

284

2) 72 = 2^3*3^2

so n should have 2^2 and 3

so largest possible integer that must divide n is 12 (its largest see the word must)

yup ... elaborating on wht u said ...
if we take 24 ... then it will not satisfy for 12^2
285
Guys,

Is it always true that in a right angled triangle inscribed in a circle, the hypotenuse is always the diameter??



Yes its always true



Is it possible to construct a right-triangle inscribed in a circle, where the hypotenuse is not the diameter??


Not possible
286
Guys,

Is it always true that in a right angled triangle inscribed in a circle, the hypotenuse is always the diameter??

Is it possible to construct a right-triangle inscribed in a circle, where the hypotenuse is not the diameter??


warrior has already answered your question but there is also a certain geometery proof that you can look up if you interested

The angle subtended by the diameter at any point on a circle is always equal to Ninety Degrees


p.s. For one who is weak in geometry, I am rather pleased with myself right now
287

Guys could you plz post the ans and explns for these ques??

1) A certain university will select 1 of 7 candidates eligible to fill a position in the mathematics department and 2 of 10 candidates eligible to fill 2 identical positions in the computer science department. If none of the candidates is eligible for a position in both departments, how many different sets of 3 candidates are there to fill the 3 positions?
A. 42
B. 70
C. 140
D. 165
E. 315

2) The points R, T, and U lie on a circle that has radius 4. If the length of arc RTU is (4 * pi) / 3, what is the length of line segment RU?
A. 34
B. 38
C. 3
D. 4
E. 6

3) Mary persuaded n friends to donate $500 each to her election campaign, and then each of these n friends persuaded n more people to donate $500 each to Mary's campaign. If no one donated more than once and if there were no other donations, what was the value of n?
(1) The first n people donated 161 of the total amount donated.
(2) The total amount donated was $120,000.

4) If n is a positive integer, what is the remainder when 3^ (8n+3) + 2 is divided by 5?
A. 0
B. 1
C. 2
D. 3
E. 4

5) If p is the product of the integers from 1 to 30, inclusive, what is the greatest integer k for which 3k is a factor of p?
A. 10
B. 12
C. 14
D. 16
E. 18

6) If x and y are positive, is x^3 > y?
(1) x > y
(2) x > y

7) If x, y, and k are positive numbers such that (x/(x+y))(10) + (y/(x+y)(20) = k and if x A. 10
B. 12
C. 15
D. 18
E. 30

Each of the 30 boxes in a certain shipment weighs either 10 pounds or 20 pounds, and average (arithmetic mean) weight of the boxes in the shipment is 18 pounds. If the average weight of the boxes in the shipment is to be reduced to 14 pounds by removing some of the 20-pound boxes, how many 20-pound boxes must be removed?
A. 4
B. 6
C. 10
D. 20
E. 24

288
Guys could you plz post the ans and explns for these ques??

1) A certain university will select 1 of 7 candidates eligible to fill a position in the mathematics department and 2 of 10 candidates eligible to fill 2 identical positions in the computer science department. If none of the candidates is eligible for a position in both departments, how many different sets of 3 candidates are there to fill the 3 positions?
A. 42
B. 70
C. 140
D. 165
E. 315

2) The points R, T, and U lie on a circle that has radius 4. If the length of arc RTU is (4 * pi) / 3, what is the length of line segment RU?
A. 34
B. 38
C. 3
D. 4
E. 6

3) Mary persuaded n friends to donate $500 each to her election campaign, and then each of these n friends persuaded n more people to donate $500 each to Marys campaign. If no one donated more than once and if there were no other donations, what was the value of n?
(1) The first n people donated 161 of the total amount donated.
(2) The total amount donated was $120,000.

4) If n is a positive integer, what is the remainder when 3^ (8n+3) + 2 is divided by 5?
A. 0
B. 1
C. 2
D. 3
E. 4

5) If p is the product of the integers from 1 to 30, inclusive, what is the greatest integer k for which 3k is a factor of p?
A. 10
B. 12
C. 14
D. 16
E. 18

6) If x and y are positive, is x^3 > y?
(1) x > y
(2) x > y

7) If x, y, and k are positive numbers such that (x/(x+y))(10) + (y/(x+y)(20) = k and if x A. 10
B. 12
C. 15
D. 18
E. 30

Each of the 30 boxes in a certain shipment weighs either 10 pounds or 20 pounds, and average (arithmetic mean) weight of the boxes in the shipment is 18 pounds. If the average weight of the boxes in the shipment is to be reduced to 14 pounds by removing some of the 20-pound boxes, how many 20-pound boxes must be removed?
A. 4
B. 6
C. 10
D. 20
E. 24


1) maths can be selected in 7 ways

comp sci in 10C2 = 45

so total = 45*7 =315

2) circumferenc e= 8 8pi

so RTU angle at center = 4*pi/3/8*pi = pi/6 = 30

now use cosine law but none of the ans are matching

3) total person p= 1+n+n^2

so toal amount = p*500

I dint get the 1st condition

usning 2nd you can find out n

4) 3 follows cycle of 4 when last digit is concerned

3^1 =3
3^2= 9
3^3=27
3^4=81


so 3^(8n+3) will always end in 7

so 7+2 = 9

rem = 4

5) its 14

30/3= 10
10/3 =3
3/3=1

add all the quote we get 14

6) both condition are same check the qn again

baaki next post mein
289

7) If x, y, and k are positive numbers such that (x/(x+y))(10) + (y/(x+y)(20) = k and if x A. 10
B. 12
C. 15
D. 18
E. 30

Each of the 30 boxes in a certain shipment weighs either 10 pounds or 20 pounds, and average (arithmetic mean) weight of the boxes in the shipment is 18 pounds. If the average weight of the boxes in the shipment is to be reduced to 14 pounds by removing some of the 20-pound boxes, how many 20-pound boxes must be removed?
A. 4
B. 6
C. 10
D. 20
E. 24



7) you will have 10(x+y/x+y) +10y/x+y

take x= y/p where p>1

sub we get

10 + 10p/p+1

take p = 4 you will get 18

initally they have 10 pounds box = 6 and 20 pounds as 24

now they have removed 20 pounds and avd reduced to 14

new ratio of 10 and 20 pounds is 3:2 but 10 pounds remained the same so

3--6
2--4

so he has removed 20 boxes
290

Hi,
I saw few Math problems in some old thread and don't have answers posted.

Here is one of them.

A tank of 425 litres capacity has been filled using two pipes, the first pipe having been opened 5 hrs longer than the second.If the first pipe were to open as long as the second and the second pipe was open as long as the first then the the first pipe would deliver half the amount of water delivered by the second pipe;if the two pipes were opened simultaneously,the tank would be filled up in 17 hours.How long was the second pipe open?
a)10 hrs
b)12 hrs
c)15 hrs
d)18 hrs

I solved it and getting approximately 15 hrs. Can anyone post the answer for this pls.

291

Yes, its always true...I guess

292
Hi,
I saw few Math problems in some old thread and don't have answers posted.

Here is one of them.

A tank of 425 litres capacity has been filled using two pipes, the first pipe having been opened 5 hrs longer than the second.If the first pipe were to open as long as the second and the second pipe was open as long as the first then the the first pipe would deliver half the amount of water delivered by the second pipe;if the two pipes were opened simultaneously,the tank would be filled up in 17 hours.How long was the second pipe open?
a)10 hrs
b)12 hrs
c)15 hrs
d)18 hrs

I solved it and getting approximately 15 hrs. Can anyone post the answer for this pls.


yeah, pallavi.. you are right! even i think ans is c) 15 hrs....

Let P1 & P2 be the rates at which pipe 1 and pipe 2 are filling water. Let t be the time taken by pipe 2. So, solve for t from

425 = P1(t+5) + t*P2
425 = P1*t + p2 * t (replace p2 with 2*p1 as suggested in ques)
425 = (P1 + P2) 17
ans - t = 15hrs

cheers,
lizzy
:
293

Hai every one.

294

Guys,
Please help me with this problem :-

If a circle, regular hexagon and a regular octagon have the same area and if the perimeter of the circle is represented by "c", that of the hexagon by "h" and that of the octagon by "o", then which of the following is true?

a)c > o > h
b)c > h > o
c)h > c > o
d)o > h > c
e)h > o > c

Cheers,
Lizzy
...............................................................................
***You won't need pockets in the last suit you wear***
...............................................................................

295
A----------B---------C----------D

Is
CD > BC ?
(1) AD = 20
(2) AB = CD


A Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D EACH Statement ALONE is sufficient.
E Statements (1) and (2) TOGETHER are NOT sufficient.

I would choose choice E.As,Statement (1) alone is not sufficient,tjis leaves with choices B,C or E.
Choice (2) alone is not sufficient therefore choice B is ruled out.We cannot conclude from the data ,the values of AB,BC or CD.therefore the answer is E.
296
If a circle, regular hexagon and a regular octagon have the same area and if the perimeter of the circle is represented by "c", that of the hexagon by "h" and that of the octagon by "o", then which of the following is true?

a)c > o > h
b)c > h > o
c)h > c > o
d)o > h > c
e)h > o > c


the answer would be E, no tricks here, just some darned mensuration, Area of circke is 'pi*r^2' so in terma of area perimeter is 2 (A*pi)^(1/2)

for regular hexagon, perimeter in terms of area is 2 (2*root 3*A)^(1/2)

for octagon, area in terms of side is 2(root 2 + 1)* square of side, hence perimeter in terms of area 2 (8(root 2 - 1)*A)^(1/2)

if you know values of pi, root 2 and root 3, you can compare these since A is common for ll three, giving h >o >c


PS- please excuse the clumsy way in which I typed these expressions
297

E...Nothing can be inferred from the information given

298

Hi, Can someone help me with this?

If M and N are positive integers that have remainders of 1 & 3 respectively when divided by 6, which of the following could not be a possible value of M+N?

A) 86
B. 52
C. 34
D. 28
E. 10

Pls post your answer with explanations

299
Hi, Can someone help me with this?

If M and N are positive integers that have remainders of 1 & 3 respectively when divided by 6, which of the following could not be a possible value of M+N?

A) 86
B. 52
C. 34
D. 28
E. 10

Pls post your answer with explanations

IMO the answer should be E.
The possible values for M r 7,13,19,25,...
The possible values for N r 9,15,21,27,...
Since the sum of their least possible values, 7+9=16 .The least valu possible should be 16.Therefore a value of 10 is not possible.
300
7) you will have 10(x+y/x+y) +10y/x+y

take x= y/p where p>1

sub we get

10 + 10p/p+1

take p = 4 you will get 18

initally they have 10 pounds box = 6 and 20 pounds as 24

now they have removed 20 pounds and avd reduced to 14

new ratio of 10 and 20 pounds is 3:2 but 10 pounds remained the same so

3--6
2--4

so he has removed 20 boxes

How do u get k=18,when u substitute p=4?I solves to k=10.