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Problem Solving (PS) | Re: A circular gear with a diameter of 24 centimeters is mounted directly

September 29, 2023, 11:49 pm
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very easy -600-650 level

ratio of diameter=big:small=4:1
ratio of speed=big:small=1:4

now the direction movement is opposite--->at meeting point a total of angle of 360 degree would have been covered by both(360=0degree ;similar to initial condition);
since ratio of speed is 4:1 similar will be the ratio of angle subttended.
so from above
5x=360
x=72
so we are required to find meeing distance of second time meeting point
similarly, next meeting at 72 degree again
now,
total degree covered by big gear =72(1st meet)+72(2nd meet)=144

now distance=144/360*pi*dia(big gear)=38.4pi
hence (C)

Statistics : Posted by SAHILBISHT0603 • on 01 Aug 2013, 10:06 • Replies 13 • Views 11884

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Problem Solving (PS) | Re: An integer N is selected at random in the range 1 N 2020. What is

September 29, 2023, 11:56 pm
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↧↧↧ Detailed Video Solution to the Problem↧↧↧

Iframe


Given that An integer N is selected at random in the range 1 ≤ N ≤ 2020. What is the probability that the remainder when N^16 is divided by 5 is1?

Theory : To find the remainder of a number by 5, we can just find the remainder of the unit's digit of the number by5
(Watch thisvideo to Learn the DivisibilityRules )

Since we need to get a remainder of 1 after dividing by 5 => the unit's digit can be
0 + 1 and 5 + 1 = 1 and 6 respectively

Let's look at all the numbers’ from 1 to 10 and see whose\(16^{th}\) power can give us 1 or 6 as the unit's digit

Unit's digit of any power of 1 will always be 1 => 1^16 will give 1 remainder when divided by 1 =>POSSIBLE
=>\(16^{th}\) power of any number with 1 as the unit's digit will give 1 remainder when divided by 5

Unit's digit of power of 2 will be 2, 4, 8, 6, 2, 4.... => They repeat after 4 => Unit's digit of 2^16 =
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Statistics : Posted by BrushMyQuant • on 20 May 2022, 01:30 • Replies 5 • Views 2341

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Problem Solving (PS) | Re: Data sets X and Y each consist of 4 values, as shown in the table. If

September 30, 2023, 12:01 am
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Values of Data Set Y = (Values of Data Set X * 5) + 16

Range = Highest Value - Lowest Value

So, Range of Set Y = Highest Value of Set Y - Lowest Value of Set Y
= Highest Value of Set X*5 + 16 - ( Lowest Value of Set X*5 + 16 )
= Highest Value of Set X*5 + 16 - Lowest Value of Set X*5 - 16
= Highest Value of Set X*5 - Lowest Value of Set X*5
= 5 * (Highest Value of Set X- Lowest Value of Set X)
= 5 * Range of Set X = 5*21 = 105

So, Answer will be E
Hope it helps!

Watch the following video to Learn the Basics of Statistics

Iframe

Statistics : Posted by BrushMyQuant • on 23 Jun 2022, 20:00 • Replies 3 • Views 620

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Problem Solving (PS) | Re: Ahab ran southeast at 10 km per hour. An hour later, Eli ran southeast

September 30, 2023, 12:08 am
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Dear ExpertsKarishmaB Bunuel GMATNinja
Please check if my method is correct

As we know Distance = Speed x Distance
Let x be the time taken by Ahab and D is the total distance

Equation for Ahab:
10*x =D

Equation for Eli:
15*(x-1.5) = D
here 1.5 = 1 (Eli started 1 hourlate) + 0.5 (Eli reached 0.5 hoursearly)

So 10*x =15(x-1.5) , which gives x = 4.5 hours
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Attachments 20230930_112857.jpg
20230930_112857.jpg [ 806.27 KiB | Viewed 45 times ]

Statistics : Posted by hemilshihora • on 20 Jul 2023, 11:16 • Replies 5 • Views 893

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Data Sufficiency (DS) | Re: Three friends, A, B and C have houses along a straight road, in that

September 30, 2023, 12:12 am
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Statistics : Posted by bumpbot • on 19 Jul 2018, 00:29 • Replies 8 • Views 4837

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Problem Solving (PS) | Re: A tank has both an inlet pipe and an outlet pipe. Working

September 30, 2023, 12:52 am
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Statistics : Posted by bumpbot • on 20 Jan 2014, 08:24 • Replies 9 • Views 16566

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Problem Solving (PS) | Re: A work is done by 30 workers not all of them have the same capacity to

September 30, 2023, 12:55 am
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Statistics : Posted by bumpbot • on 02 Dec 2020, 12:30 • Replies 5 • Views 16335

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Data Sufficiency (DS) | Re: Each person attending a fund-raising party for a certain club was

September 30, 2023, 1:01 am
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Statistics : Posted by bumpbot • on 23 Sep 2010, 12:15 • Replies 9 • Views 30887

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Data Sufficiency (DS) | Re: If l1 and l2 are distinct lines in the xy coordinate system such that

September 30, 2023, 1:33 am
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gmatophobia can you elaborate the explanation for statement 2 with a suitable diagram ?

Statistics : Posted by Can,Will • on 03 Jan 2016, 13:53 • Replies 8 • Views 4434

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Data Sufficiency (DS) | Re: In a certain institute, every student studies at least one of two subj

September 30, 2023, 2:36 am
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Statistics : Posted by bumpbot • on 10 Jul 2017, 04:27 • Replies 5 • Views 2503

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Problem Solving (PS) | Re: The velocity of a propelled object is described by the equation v=v0+a

September 30, 2023, 2:48 am
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Statistics : Posted by bumpbot • on 01 Sep 2020, 01:20 • Replies 8 • Views 3258

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Data Sufficiency (DS) | Re: A family's savings for a month is calculated by subtracting its total

September 30, 2023, 2:56 am
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Statistics : Posted by bumpbot • on 21 Jul 2018, 11:03 • Replies 2 • Views 1338

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Problem Solving (PS) | Re: Sequence S is defined as Sn = X + (1/X), where X = Sn 1 + 1

September 30, 2023, 6:41 am
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Statistics : Posted by bumpbot • on 23 Jan 2020, 02:19 • Replies 5 • Views 7149

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GMAT Club Tests | D01-31

September 30, 2023, 6:53 am
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Bunuel

I solved this question by 4*10=40 (initial amount) and I increased the prop by double 8*5=40. I am not sure if this logic is right or not. Kindly help me with this.

Statistics : Posted by Rakshit99 • on 16 Sep 2014, 00:13 • Replies 9 • Views 76487

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Problem Solving (PS) | Re: A housing subdivision contains only two types of homes: ranch-style ho

September 30, 2023, 6:57 am
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Statistics : Posted by bumpbot • on 21 May 2017, 12:57 • Replies 6 • Views 3252

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Quantitative | Re: Viete's Theorem vs MGMAT factoring approach: +/- b?

September 30, 2023, 7:18 am
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Statistics : Posted by bumpbot • on 12 Apr 2021, 16:45 • Replies 3 • Views 1170

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Data Sufficiency (DS) | Re: Solution A costs $5 per litre and Solution B costs $9 per litre. If p

September 30, 2023, 7:57 am
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RenB wrote:

Solution A costs $5 per litre and Solution B costs $9 per litre. If p litres of Solution A and q litres of solution B are used to make 5 litres of solution C, is p > q?

(1) q<3.

(2) 5 litres of solution C costs less than$30.


From the question stem we can infer that-

\( p + q =5\)

Statement1

(1)q<3

If q = p = 2.5 → The response to the question, is p > q , is No.

If p = 0.1 , q = 4.9 → The response to the question, is p > q , is Yes.

As we are getting two contracting responses to the question. The statement alone is not sufficient and we can eliminate A and D.

Statement2

(2) 5 litres of solution C costs less than$30

\( 5p + 9q <30\)

There are couple of ways to solve this -

1) We can use the information\( p + q =5\) to find the maximum value of p.
2) Plug in some smart values to the inequality and infer the result.

Let's use method2

\( 5p + 9q <30\)

We know that the values of\(p\) and\(q\) are equal when\( p = q =2.5\)

Let's assume\( p = q =2.5\)

Cost of Solution
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Statistics : Posted by gmatophobia • on 30 Sep 2023, 06:10 • Replies 1 • Views 64

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Problem Solving (PS) | Re: What is the probability that a point satisfying the conditions |x|

September 30, 2023, 8:03 am
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hadimadi wrote:

Hi Rajshek,

the total area filled by the conditions for x,y is 2*2 per quadrant. We have 4 quandrants, so its 4^2=16.
Now, how much of that area is occupied with Ix+yI<=1?
For that, check the picture that nick posted.
Now, if you draw the square (4x4 square) into the coordinate system, and also draw the stuff that nick posted, you can see that two equal triangles are created. Each has two sides of length 3 (a,b, hypotenuse c leave open, u dont need it now).

So in total, the two triangles take 3*3=9 of the area.
This means that 9/16 is free -> 7/16 is occupied.


i didn't get how do u take 2*2 per quadrant?please explain ...I'm unable to understand it

Statistics : Posted by pudu • on 21 Oct 2019, 17:07 • Replies 13 • Views 3387

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Problem Solving (PS) | Re: Three pipes A, B and C can fill a tank in 10, 15 and 25 minutes respec

September 30, 2023, 8:09 am
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Hello from the GMAT Club BumpBot!

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Statistics : Posted by bumpbot • on 23 Nov 2018, 06:57 • Replies 11 • Views 9058

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Data Sufficiency (DS) | Re: A certain building has only 2-room and 3-room apartments to rent. If

September 30, 2023, 8:15 am
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Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Statistics : Posted by bumpbot • on 23 Jul 2019, 08:00 • Replies 5 • Views 4979

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