Problem Solving (PS) | Re: In 2008, the total revenue from movies was 842.1 million dollars. If R

July 12, 2024, 8:58 pm

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Hello from the GMAT Club BumpBot!

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Statistics : Posted by bumpbot • on 10 Feb 2022, 03:30 • Replies 3 • Views 3301

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Problem Solving (PS) | Re: (159,919)/((409)*(17))

July 12, 2024, 8:58 pm

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Statistics : Posted by bumpbot • on 05 Mar 2017, 11:42 • Replies 15 • Views 7976

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Problem Solving (PS) | Re: If 8^c8 = 8^a/8^b then a = ?

July 12, 2024, 9:05 pm

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Statistics : Posted by bumpbot • on 10 Feb 2022, 03:45 • Replies 2 • Views 1944

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Problem Solving (PS) | Re: If |x + 5| = 3 and |2y - 1|/3 = 5, then |x + y| could equal each of th

July 12, 2024, 9:12 pm

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Statistics : Posted by bumpbot • on 20 Jul 2018, 00:13 • Replies 4 • Views 7621

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Problem Solving (PS) | Re: Eight teams participate in a tournament and each team plays exactly on

July 12, 2024, 10:30 pm

≫ Next: Problem Solving (PS) | Re: In a race of 500 m, L beats M by 40 seconds and beats N by 125 m. If M

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The question too sophisticated and ambiguous to be in the GMAT since two teams can be also have equal points and in that case we cannot say that A has more POINTS than B and C. But if we say that 8 teams are ranked and in how many ways can A be ranked above both B and C, only under this assumption can we say the answer is choice C

Statistics : Posted by 8Harshitsharma • on 27 Apr 2020, 02:04 • Replies 3 • Views 13805

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Problem Solving (PS) | Re: In a race of 500 m, L beats M by 40 seconds and beats N by 125 m. If M

July 12, 2024, 10:33 pm

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L-M = 40 seconds
L-N =125 Mts ......................(1)
M-N = 40 seconds ....................(2)

Hence, L-N= 80 seconds ...................(3)

So from (1) and (3), N takes 80 seconds to cover 125 mts.
Time taken to by N cover 125 mts = 80 seconds
Time taken by N to cover 500 mts = 320 seconds

From (2) M takes 40 seconds Less than N to cover 500 mts.

So M takes 280 seconds.

C

Statistics : Posted by Dooperman • on 01 Jun 2020, 09:33 • Replies 14 • Views 7096

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Problem Solving (PS) | Re: Machine A, working alone at a constant rate, can complete a certain

July 12, 2024, 11:39 pm

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Statistics : Posted by bumpbot • on 23 Jun 2019, 07:17 • Replies 6 • Views 7740

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Problem Solving (PS) | Re: Of the seminar classes at a certain university, 65% have 15 or fewer

July 13, 2024, 12:08 am

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Problem Solving (PS) | Re: Tap A can fill the cistern in 40 hours and tap B is an inlet pipe with

July 13, 2024, 12:14 am

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Problem Solving (PS) | Re: There are 2 decks of cards. The first deck has a 100 cards labelled...

July 13, 2024, 12:40 am

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From 1 to 100: (Note that the greatest multiple of 7 is 98 and the smallest multiple of 7 is 7.)
=> (98 - 7)/7+ 1 = 91/7 + 1 = 14 multiples of 7

From 101 to 250: (Note that the greatest multiple of 7 is 245 and the smallest multiple of 7 is 105.)
=> (245 - 105)/7+ 1 = 140/7 + 1 = 21 multiples of 7

Thus, The probability of selecting a multiple of 7 in the first set of cards is 14/100, and in the second set it is 21/150.

Now, The probability that both selected cards will contain multiples of 7,
so we multiply the two probabilities to determine the total probability: 14/100 x 21/150 = (14 x 21)/(100 x 150) = (7 x 7)/(50 x 50) = 7^2/2500.

Answer: E

Statistics : Posted by A_Nishith • on 03 Feb 2015, 19:03 • Replies 6 • Views 5761

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Problem Solving (PS) | Re: If m is the product of all integers from 1 to 40, inclusive

July 13, 2024, 12:46 am

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July 13, 2024, 1:07 am

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Problem Solving (PS) | Re: If x = 1 + 5^(1/3) + 5^(2/3), then the value of x^3 - 3x^2 - 12x + 6

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Problem Solving (PS) | Re: If two numbers are selected randomly from the first 100 natural number

July 13, 2024, 1:50 am

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Problem Solving (PS) | Find the greatest integer less than or equal to k

July 13, 2024, 2:32 am

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↧↧↧ Detailed Video Solution to the Problem↧↧↧

Iframe

Given that\( 34 - |x^2 - 3x + 8| \leqk\) and we need to find the greatest integer less than or equal tok

Now on the left hand side we have 34 - | Of a Number | and we need to find the greatest possible value of thisexpression.
| Of a Number | will benon-negative
=> The output of | of a Number | will anyways get subtracted from 34 and will reduce the overall value.
So, the idea is to make the value inside the Absolute Valueminimum

\( |x^2 - 3x +8|\) = \( |x^2 -2*\frac{3}{2} *x +(\frac{3}{2} )^2 -(\frac{3}{2} )^2 +8|\)
= \( |(x -\frac{3}{2} )^2 + 8 -\frac{9}{4}|\) = \( |(x -\frac{3}{2} )^2 +\frac{23}{4}|\)

Now, this will be minimumwhen \( (x -\frac{3}{2})^2\) =0
=> x= \(\frac{3}{2}\)

=> \( 34 - |x^2 - 3x + 8| \leqk\) = \( 34 - |0 +\frac{23}{4} | \leqk\) = \( 34 - |5.75| \leqk\)= \( 34 - 5.75 \leqk\) =\( 28.25 \leqk\)
=> k = 28[ Greatest Possbile Integer less than or equal to k ]

So, Answer will beB
Hope ithelps!

Watch the following video to Master AbsoluteValues

Iframe
...

Statistics : Posted by BrushMyQuant • on 25 Nov 2020, 19:45 • Replies 3 • Views 2973

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Problem Solving (PS) | Re: The number of ways a lawn tennis mixed doubles match can be made up of

July 13, 2024, 2:46 am

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Statistics : Posted by bumpbot • on 05 Jan 2014, 19:00 • Replies 2 • Views 7344

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Problem Solving (PS) | In a certain TV game show, exactly 1 prize was placed behind each of 6

July 13, 2024, 2:58 am

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My solution:
The probability that the winning prize is behind one of the curtains is 2/6 (let's say A).
The probability that another winning prize is behind another specific curtain is 1/5 (let's say D).

The probability of these two together is 2/6 * 1/5= 2/30.

There are 3 scenarios for this to happen so 3*2/30 = 1/5 (AD, BE, CF)

Statistics : Posted by korteraz • on 29 Oct 2023, 10:45 • Replies 8 • Views 5192

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Problem Solving (PS) | Re: The sum of x numbers is what percent greater than the average

July 13, 2024, 3:10 am

≫ Next: Problem Solving (PS) | Re: A furniture dealer purchased a sofa and an armchair for the same

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Sum = AVG * Number of Items

Percent change formula: 100* (Final value - Initial value) / Initial value

100*(X*AVG - AVG) / AVG = 100*(X - 1)

Statistics : Posted by korteraz • on 09 Mar 2024, 01:28 • Replies 5 • Views 2594

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Problem Solving (PS) | Re: A furniture dealer purchased a sofa and an armchair for the same

July 13, 2024, 3:28 am

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Let x = the cost of the armchair and the sofa.

The profit on the armchair is 10% of the cost of the armchair = X/10
The revenue from the armchair is given by the formula: Revenue - Expenses = Profit => Revenue - X = X/10 =>
Revenue = 11x/10

The revenue from the sofa is 20% more than from the armchair = (120/100) * (11x/10) = 132x/100

The profit(revenue - expenses) from the sofa is (132x/100) - x = 32x/100

Percentage change formula: 100*(final - initial) / initial

100*(32x/100 - x/10) / x/10 = 100*((32 - 10)/100) / (1/10) = 22 / (1/10) = 220

Statistics : Posted by korteraz • on 28 Oct 2023, 17:23 • Replies 3 • Views 3062

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