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Users' Self Made Questions 05 Dec 2017, 09:04
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Users' Self Made Questions Updated on: 07 Oct 2019, 16:03
Originally posted by Hovkial on 05 Oct 2019, 15:09.
Last edited by Hovkial on 07 Oct 2019, 16:03, edited 2 times in total.
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X, Y and Z are three non-negative integers such that X+Y+Z = 36. How many solutions are possible for this equation where \(X >= Y\) (i.e., X is greater than or equal to Y)?

(A) 319

(B) 341

(C) 361

(D) 385

(E) 405

EDIT:

(1) Corrected from "positve integers" to "non-negative integers".
(2) Added: X greater than or equal to Y.
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Users' Self Made Questions 06 Oct 2019, 09:53
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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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RESERVED................................
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Users' Self Made Questions 05 Dec 2017, 09:06
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Triangle ABC is a right angled triangle with right angle at Vertex B. Triangle DEF is an equilateral triangle with side 10 cm. The lengths of sides (in cm) are marked in the Drawing. What is the area of the polygon ABFEGA?

(1) The length of CD (overlap of sides) is 3 cm.
(2) The length of altitude (GH) of triangle GDC is 2.598 cm.


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D

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Attachment:
Triangle.jpg
Triangle.jpg [ 14.35 KiB | Viewed 13543 times ]
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Users' Self Made Questions 05 Dec 2017, 19:00
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Hi math experts, try this question and provide feedback...

Janvisahu

Triangle ABC is a right angled triangle with right angle at Vertex B. Triangle DEF is an equilateral triangle with side 10 cm. The lengths of sides (in cm) are marked in the Drawing. What is the area of the polygon ABFEGA?

(1) The length of CD (overlap of sides) is 3 cm.
(2) The length of altitude (GH) of triangle GDC is 2.598 cm.


Show SpoilerOA
D

Show Spoiler
Attachment:
Triangle.jpg
Show more
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rahul16singh28
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Users' Self Made Questions 05 Dec 2017, 19:27
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Janvisahu
Hi math experts, try this question and provide feedback...

Janvisahu

Triangle ABC is a right angled triangle with right angle at Vertex B. Triangle DEF is an equilateral triangle with side 10 cm. The lengths of sides (in cm) are marked in the Drawing. What is the area of the polygon ABFEGA?

(1) The length of CD (overlap of sides) is 3 cm.
(2) The length of altitude (GH) of triangle GDC is 2.598 cm.


Show SpoilerOA
D

Show Spoiler
Attachment:
Triangle.jpg
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Hi Janvisahu,

Should be D.

From Stmnt 1: Angle BCA = 60. Hence Triangle, GDC is equilateral Triangle. So, Sufficient.

From Stmnt 2: Triangle ABC is Similar to Triangle GHC. Using this you can find the length of GC. So, Sufficient.

Hope this Helps.
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Users' Self Made Questions 05 Dec 2017, 20:42
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Janvisahu
Hi math experts, try this question and provide feedback...

Janvisahu

Triangle ABC is a right angled triangle with right angle at Vertex B. Triangle DEF is an equilateral triangle with side 10 cm. The lengths of sides (in cm) are marked in the Drawing. What is the area of the polygon ABFEGA?

(1) The length of CD (overlap of sides) is 3 cm.
(2) The length of altitude (GH) of triangle GDC is 2.598 cm.


Show SpoilerOA
D

Show Spoiler
Attachment:
Triangle.jpg

Hi Janvisahu,

Should be D.

From Stmnt 1: Angle BCA = 60. Hence Triangle, GDC is equilateral Triangle. So, Sufficient.

From Stmnt 2: Triangle ABC is Similar to Triangle GHC. Using this you can find the length of GC. So, Sufficient.

Hope this Helps.
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How could you come to the conclusion that angle BCA is 60 degrees from statement 1??

Posted from my mobile device
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Users' Self Made Questions 05 Dec 2017, 20:45
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Hi
Very nice work.
I have framed this question myself. If you think, this is a good question, please provide Kudos...

\(\)
rahul16singh28
Janvisahu
Hi math experts, try this question and provide feedback...

Janvisahu

Triangle ABC is a right angled triangle with right angle at Vertex B. Triangle DEF is an equilateral triangle with side 10 cm. The lengths of sides (in cm) are marked in the Drawing. What is the area of the polygon ABFEGA?

(1) The length of CD (overlap of sides) is 3 cm.
(2) The length of altitude (GH) of triangle GDC is 2.598 cm.


Show SpoilerOA
D

Show Spoiler
Attachment:
Triangle.jpg

Hi Janvisahu,

Should be D.

From Stmnt 1: Angle BCA = 60. Hence Triangle, GDC is equilateral Triangle. So, Sufficient.

From Stmnt 2: Triangle ABC is Similar to Triangle GHC. Using this you can find the length of GC. So, Sufficient.

Hope this Helps.
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Users' Self Made Questions 05 Dec 2017, 20:49
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Janvisahu
Hi math experts, try this question and provide feedback...

Janvisahu

Triangle ABC is a right angled triangle with right angle at Vertex B. Triangle DEF is an equilateral triangle with side 10 cm. The lengths of sides (in cm) are marked in the Drawing. What is the area of the polygon ABFEGA?

(1) The length of CD (overlap of sides) is 3 cm.
(2) The length of altitude (GH) of triangle GDC is 2.598 cm.


Show SpoilerOA
D

Show Spoiler
Attachment:
Triangle.jpg
Show more

Sin C = \(8/16/\sqrt{3}\)
C = 60.
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Users' Self Made Questions 05 Dec 2017, 20:51
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Hi
It is easy to prove that angle BCA is 60.
triangle ABC is 30:60:90 triangle as we know by the ration of sides.
Sides are in ratio-1:root 3:2




Janvisahu

Triangle ABC is a right angled triangle with right angle at Vertex B. Triangle DEF is an equilateral triangle with side 10 cm. The lengths of sides (in cm) are marked in the Drawing. What is the area of the polygon ABFEGA?

(1) The length of CD (overlap of sides) is 3 cm.
(2) The length of altitude (GH) of triangle GDC is 2.598 cm.


Show SpoilerOA
D

Show Spoiler
Attachment:
Triangle.jpg
Show more
[/quote]

Hi Janvisahu,

Should be D.

From Stmnt 1: Angle BCA = 60. Hence Triangle, GDC is equilateral Triangle. So, Sufficient.

From Stmnt 2: Triangle ABC is Similar to Triangle GHC. Using this you can find the length of GC. So, Sufficient.

Hope this Helps.[/quote]


How could you come to the conclusion that angle BCA is 60 degrees from statement 1??

Posted from my mobile device[/quote]
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Users' Self Made Questions 09 Dec 2017, 23:07
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New Question



The square of the median of a sequence of consecutive positive odd integers is equal to the difference between the squares of the first and last terms. If the sequence has twelve terms, what is the sum of the digits of the first and last terms?

A. 12
B. 16
C. 20
D. 24
E. 28


source:self

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B
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Users' Self Made Questions 09 Dec 2017, 23:52
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gracie
The square of the median of a sequence of consecutive positive odd integers is equal to the difference between the squares of the first and last terms. If the sequence has twelve terms, what is the sum of the digits of the first and last terms?

A. 12
B. 16
C. 20
D. 24
E. 28


source:self
Show more
The median of 12 consecutive odd integers is between the 6th and 7th terms, where if \(n > 1\), then
\(A_{n} = A_1 + 2(n-1)\)

\(A_1 = n\)
\(A_2 = n + 2\)
.
.
\(A_6 = n + 10\)
\(A_7 = n + 12\)
.
.
\(A_{12} = n + 22\)

Median = \(n + 11\). If not sure:

\(\frac{(n+10+n+12)}{2}=\frac{(2n+22)}{2}=(n + 11)\)

Square of median = difference between squares of first and last terms:

\((n + 22)^2 - (n)^2 = (n + 11)^2\)
\(n^2 + 44n + 484 - n^2 = n^2 + 22n + 121\)
\(n^2 - 22n - 363 = 0\)
\((n - 33)(n + 11) = 0\)
\(n = 33\) (prompt says positive)

\(A_1 = 33\)
\(A_{12} = n + 22 = 55\)

Sum of digits of \(33\) and \(55\):
\(3 + 3 + 5 + 5 = 16\)

ANSWER B
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Users' Self Made Questions 14 Dec 2017, 07:15
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New Question:

If from a well-shuffled deck of 52 cards, five cards are drawn at random one by one with replacement. What is the probability of fifth card being spade?
A) 1/3
B) 1/4
C) 2/5
D) 3/13
E) 3/26

source:self

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B
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Users' Self Made Questions 16 Dec 2017, 08:18
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Challenging Question:- Earn kudos for correct solution :cool:

If from a well-shuffled deck of 52 cards, five cards are drawn at random one by one WITHOUT replacement. What is the probability of fifth card being spade?
A) 1/3
B) 1/4
C) 2/5
D) 3/13
E) 3/26

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OA - B
source:self
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Users' Self Made Questions 17 Dec 2017, 09:38
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You might like this problem...

gmatbusters
Challenging Question:- Earn kudos for correct solution :cool:

If from a well-shuffled deck of 52 cards, five cards are drawn at random one by one WITHOUT replacement. What is the probability of fifth card being spade?
A) 1/3
B) 1/4
C) 2/5
D) 3/13
E) 3/26

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Users' Self Made Questions 19 Dec 2017, 22:52
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This question can be done by two methods, first being conventional method, in which we will find conditional probabilities when the cards drawn in earlier draw is spade or not spade and adding all the cases.
But this method is tedious and lengthy.

My approach:
Since the number of cards of spade, heart, club and diamond is same.
The probability of each group of cards to appear in required draw will be same by symmetry. Let each probability be p.

Now since it is certain that the fifth card will be out of these four groups . TOTAL probability =1
p+p+p+p =1
Hence p =1/4.
Answer is 1/4.

Please provide Kudos if u like my approach.
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Users' Self Made Questions 04 Feb 2018, 11:41
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Q)How many different numbers can be formed from the products of numbers taken from set of 25 different prime numbers.(consider given is a set of first 25 prime numbers).

A. 2^25
B. 625
C. 25c2
D. 25p2
E. None of these

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=25c2+25c3+25c4+...25c25
=25c0+25c1+25c2+25c3+25c4+...25c25-(25c0+25c1)
=2^25 - 26
Answer is E.
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