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Users' Self Made Questions
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Vadodada
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Re: Users' Self Made Questions [#permalink] New post  21 Aug 2019, 04:42
A car runs on four tyres and has one extra tyre. If each tyre lasts for 10,000 km then what is the
maximum distance (in km) that the car can travel using the five tyres?
(a) 10,000 (b) 11,000 (c) 12,500 (d) 15,000

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Re: Users' Self Made Questions [#permalink] New post  12 Sep 2019, 06:14
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Find the number of odd (positive) divisors of 9!

A. 12
B. 14
C. 16
D. 18
E. 20
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Re: Users' Self Made Questions [#permalink] New post  14 Sep 2019, 08:22
nick1816 wrote:
Mr. White is an approximately forty years old father with 4 sons of distinct ages. Writing his age 3 times in succession, we get a 6-digit number that is equal to the product of his age, his wife's age and his 4 sons' ages. What is the sum of his wife's age and all 4 sons' ages?

A. 25
B. 30
C. 41
D. 51
E. 61


Well, with all the due respect, the question says approximately 40 years old. That no way signals we need to consider the age as 40 years. So I guess I will just pass and move on.
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Re: Users' Self Made Questions [#permalink] New post  14 Sep 2019, 08:39
nick1816 wrote:
Assume a 2-digit number=xy
xyxyxy=xy*a*b*c*d*e
xy(100001)=xy*a*b*c*d*e
100001=a*b*c*d*e
a*b*c*d*e=37*13*7*3*1

You actually don't need the actual age of Mr. White to solve this question.


You meant 10101*xy? I guess so.

Thank you for providing the explanation.!
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Re: Users' Self Made Questions [#permalink] New post  14 Sep 2019, 08:46
Yup. That was a typo.
Edited.

TheNightKing wrote:
nick1816 wrote:
Assume a 2-digit number=xy
xyxyxy=xy*a*b*c*d*e
xy(100001)=xy*a*b*c*d*e
100001=a*b*c*d*e
a*b*c*d*e=37*13*7*3*1

You actually don't need the actual age of Mr. White to solve this question.


You meant 10101*xy? I guess so.

Thank you for providing the explanation.!
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Re: Users' Self Made Questions [#permalink] New post  16 Sep 2019, 21:16
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nick1816 wrote:
Find 0.42-0.35

0.ab=0.ababababa......

A. \(0.7\)

B. 0.7

C. \(\frac{7}{9}\)

D. \(\frac{4}{13}\)

E. \(\frac{7}{99}\)


Options B and C are the same. What is the source of this question?
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Re: Users' Self Made Questions [#permalink] New post  16 Sep 2019, 21:24
Thanks for letting me know. Edited!!
Bunuel wrote:
nick1816 wrote:
Find 0.42-0.35

0.ab=0.ababababa......

A. \(0.7\)

B. 0.7

C. \(\frac{7}{9}\)

D. \(\frac{4}{13}\)

E. \(\frac{7}{99}\)


Options B and C are the same. What is the source of this question?
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Re: Users' Self Made Questions [#permalink] New post  16 Sep 2019, 21:30
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nick1816 wrote:
Thanks for letting me know. Edited!!
Bunuel wrote:
nick1816 wrote:
Find 0.42-0.35

0.ab=0.ababababa......

A. \(0.7\)

B. 0.7

C. \(\frac{7}{9}\)

D. \(\frac{4}{13}\)

E. \(\frac{7}{99}\)


Options B and C are the same. What is the source of this question?


Could you please tell me what is the source of this question? Thank you.
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Re: Users' Self Made Questions [#permalink] New post  16 Sep 2019, 21:51
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Seven balls of different weights are randomly painted red, orange, yellow, green, blue, indigo and violet, each ball being painted a distinct color. The green ball is found to be heavier than the blue ball, and the red ball is found to be heavier than the yellow ball.
Given just this information, if the probability that the red ball is heavier than the blue ball is a/b , where a and b are co-prime positive integers, find a + b.

A. 3
B. 5
C. 7
D. 9
E. 11
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Re: Users' Self Made Questions [#permalink] New post  16 Sep 2019, 22:57
x=0.4242.. and y=0.3535.., so Z = x-y = 0.0707...

If Z= 0.0707.. and 100Z= 7.0707.., then:
--> 100Z-Z = 7.0707.. - 0.0707..
--> 99z = 7
--> Z = 7/99

Answer is (E)
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Re: Users' Self Made Questions [#permalink] New post  17 Sep 2019, 09:39
n is a positive integer. Is \(n^3+2n\) is divisible by 12?

1) n is a prime number.
2) n>10
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Re: Users' Self Made Questions [#permalink] New post  03 Oct 2019, 23:01
The figure shows a cube of side 10 cm. If A and C are vertices of the cube and B and D are mid-points of the sides shown, what is the area of Quadrilateral ABCD?

A. \(20\sqrt{5}\)
B. \(50\sqrt{6}\)
C. \(100\sqrt{3}\)
D. 125
E. \(125\sqrt{2}\)
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Re: Users' Self Made Questions [#permalink] New post  05 Oct 2019, 19:10
Hovkial wrote:
X, Y and Z are three positive integers such that X+Y+Z = 36. How many solutions are possible for this equation?

(A) 319

(B) 341

(C) 361

(D) 385

(E) 405


number of positive integral solutions of equation x1+x2+⋯+xr=n is equal to (n-1)C(r-1)

= (36-1)C(3-1) = 35c2 = 595

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Re: Users' Self Made Questions [#permalink] New post  06 Oct 2019, 08:53
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What is the maximum value of 'N' such that the product 570 X 60 X 30 X 90 X 100 X 500 X 700 X 343 X 720 X 81 is completely divisible by \(30^N\)?

(A) 10

(B) 11

(C) 12

(D) 13

(E) 14
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Re: Users' Self Made Questions [#permalink] New post  06 Oct 2019, 11:08
X=570 X 60 X 30 X 90 X 100 X 500 X 700 X 343 X 720 X 81

30=2*3*5

The highest power of 2 that can divide X=a= 1+2+1+1+2+2+2+0+4+0=15
The highest power of 3 that can divide X=b= 1+1+1+2+0+0+0+0+2+4=11
The highest power of 5 that can divide X=c= 1+1+1+1+2+3+2+0+1+0=12

N= minimum(a,b,c)=11


Hovkial wrote:
What is the maximum value of 'N' such that the product 570 X 60 X 30 X 90 X 100 X 500 X 700 X 343 X 720 X 81 is completely divisible by \(30^N\)?

(A) 10

(B) 11

(C) 12

(D) 13

(E) 14
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Re: Users' Self Made Questions [#permalink] New post  07 Oct 2019, 01:57
Hovkial wrote:
X, Y and Z are three positive integers such that X+Y+Z = 36. How many solutions are possible for this equation?

(A) 319

(B) 341

(C) 361

(D) 385

(E) 405


Hi Hovkial

Can you post the solution ?
I think it’s 595

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Re: Users' Self Made Questions [#permalink] New post  07 Oct 2019, 15:00
We are given that:

X + Y + Z = 36.

The total number of solutions to this equation will be given by:

(36+3-1)C(3-1) = 38C2 = 703.

Note: "C" denotes combination.

The number of solutions where X will be equal to Y will be 19 [ from (X, Y) = (0, 0) to (18, 18)].

So, the number of solutions where X will not be equal to Y = 703 - 19 = 684.

Out of these 684 solutions, half of the solutions will have X > Y and the other half will have X < Y.

Hence, the total number of solutions where X will be greater than or equal to Y will be:

19 + (684/2) = 361.
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Re: Users' Self Made Questions [#permalink] New post  08 Oct 2019, 05:10
Hovkial wrote:
We are given that:

X + Y + Z = 36.

The total number of solutions to this equation will be given by:

(36+3-1)C(3-1) = 38C2 = 703.

Note: "C" denotes combination.

The number of solutions where X will be equal to Y will be 19 [ from (X, Y) = (0, 0) to (18, 18)].

So, the number of solutions where X will not be equal to Y = 703 - 19 = 684.

Out of these 684 solutions, half of the solutions will have X > Y and the other half will have X < Y.

Hence, the total number of solutions where X will be greater than or equal to Y will be:

19 + (684/2) = 361.


Why are you doing 3-1 for combination?
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Re: Users' Self Made Questions [#permalink] New post  08 Oct 2019, 05:31
nick1816

Can you elaborate your explanation?

Thank you
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Re: Users' Self Made Questions [#permalink] New post  08 Oct 2019, 05:31
X|Y|Z

Number of ways to arrange 36 similar objects and 2 lines= 38!/36!2!

or you can remember the formula

\(x_1\)+\(x_2\).....+\(x_r\)= N

where \(x_1\), \(x_2\) ....... \(x_r\) are non-negative integers

Total integral solutions= (N+r-1) C (r-1)

In the above question N=36, and r=3


Anant2410 wrote:
Hovkial wrote:
We are given that:

X + Y + Z = 36.

The total number of solutions to this equation will be given by:

(36+3-1)C(3-1) = 38C2 = 703.

Note: "C" denotes combination.

The number of solutions where X will be equal to Y will be 19 [ from (X, Y) = (0, 0) to (18, 18)].

So, the number of solutions where X will not be equal to Y = 703 - 19 = 684.

Out of these 684 solutions, half of the solutions will have X > Y and the other half will have X < Y.

Hence, the total number of solutions where X will be greater than or equal to Y will be:

19 + (684/2) = 361.


Why are you doing 3-1 for combination?
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Re: Users' Self Made Questions [#permalink]
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