Danou wrote:
When it operates at its own constant rate, hose A can fill an empty tank twice as fast as hose B can when it operates at its own constant rate. If hose A can fill the tank in x hours, how many hours will it take for the two hoses, operating simultaneously, to fill the tank?
A. 2x/3
B. 3x/2
C. 3x
D. 3/(2x)
E. 3/x
Given that hose A can fill the tank in x hours, hose B would take 2x hours to fill the tank. Thus, their combined rate is 1/x + 1/(2x) = 3/(2x). Since time is the reciprocal of rate, the two hoses operating simultaneously will take 2x/3 hours.
Answer: B.
P.S. Can you please tell me the exact source of this question? Thank you.
Statistics : Posted by Bunuel • on Apr 27, 2024 4:16 am • Replies 1 • Views 50
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Danou wrote:
When it operates at its own constant rate, hose A can fill an empty tank twice as fast as hose B can when it operates at its own constant rate. If hose A can fill the tank in x hours, how many hours will it take for the two hoses, operating simultaneously, to fill the tank?
A. 2x/3
B. 3x/2
C. 3x
D. 3/(2x)
E. 3/x
Given that hose A can fill the tank in x hours, hose B would take 2x hours to fill the tank. Thus, their combined rate is 1/x + 1/(2x) = 3/(2x). Since time is the reciprocal of rate, the two hoses operating simultaneously will take 2x/3 hours.
Answer: B.
P.S. Can you please tell me the exact source of this question? Thank you.]]>
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Statistics : Posted by bumpbot • on Mar 16, 2022 10:15 am • Replies 2 • Views 808
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gmatophobia wrote:
Bunuel wrote:
If\(\frac{\sqrt{x^2}}{\sqrt[3]{x^3}}=-1\) and\( x \neq0\) , what is the value of\( \frac{2|x| + 6}{3 -x}\) ?
A. -2
B. 1
C. 2
D. 3
E. Cannot be determined from the giveninformation
A. -2
B. 1
C. 2
D. 3
E. Cannot be determined from the giveninformation
\(\frac{\sqrt{x^2}}{\sqrt[3]{x^3}}\)
= \(\frac{|x|}{x}\)
\( \frac{|x|}{x} =-1\)
Hence, we can infer that that\(x\) is negative.
Let's assume\( x =-1\)
=\( \frac{2|x| + 6}{3 -x}\)
=\( \frac{2|-1| + 6}{3 -(-1)}\)
=\(\frac{8}{4}\)
=\(2\)
OptionC
I have a doubt. The numerator can be either postive or negative for every case of denominator can only be positive or negative.
In that case, won't the equation be always either 1 or -1. Instead of only -1. This leads to an undefined behaviourright?
Bunuel Can you pleasehelp?
\( \sqrt{x^2} =|x|\) and |x| cannot be negative. Generally, the square root sign always indicates non-negative square root.
Mathematically,\(\sqrt{...}\) is the square root sign, a function (called the principal square root function), which cannot give negative result. So, this sign(\(\sqrt{...}\) ) always means non-negative square
...
Statistics : Posted by Bunuel • on Apr 26, 2024 8:30 am • Replies 4 • Views 182
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gmatophobia wrote:
Bunuel wrote:
If\(\frac{\sqrt{x^2}}{\sqrt[3]{x^3}}=-1\) and\( x \neq0\) , what is the value of\( \frac{2|x| + 6}{3 -x}\) ?
A. -2
B. 1
C. 2
D. 3
E. Cannot be determined from the giveninformation
A. -2
B. 1
C. 2
D. 3
E. Cannot be determined from the giveninformation
\(\frac{\sqrt{x^2}}{\sqrt[3]{x^3}}\)
= \(\frac{|x|}{x}\)
\( \frac{|x|}{x} =-1\)
Hence, we can infer that that\(x\) is negative.
Let's assume\( x =-1\)
=\( \frac{2|x| + 6}{3 -x}\)
=\( \frac{2|-1| + 6}{3 -(-1)}\)
=\(\frac{8}{4}\)
=\(2\)
OptionC
I have a doubt. The numerator can be either postive or negative for every case of denominator can only be positive or negative.
In that case, won't the equation be always either 1 or -1. Instead of only -1. This leads to an undefined behaviourright?
Bunuel Can you pleasehelp?
\( \sqrt{x^2} =|x|\) and |x| cannot be negative. Generally, the square root sign always indicates non-negative square root.
Mathematically,\(\sqrt{...}\) is the square root sign, a function (called the principal square root function), which cannot give negative result. So, this sign(\(\sqrt{...}\) ) always means non-negative square
...]]>
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Statistics : Posted by bumpbot • on Oct 30, 2019 3:42 pm • Replies 4 • Views 9141
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Statistics : Posted by bumpbot • on Jul 07, 2017 9:10 am • Replies 21 • Views 25023
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Iframe
What is the smallest five-digit number which when divided by 7, 11 and 21 leaves a remainder of 5 in eachcase?
Let's solve the problem using twomethods
Method 1:Elimination
Let's subtract 5 from all the option choices so that we have numbers which are divisible by 7, 11 and 21
=> A. = 10154 (10159-4)
=> B. = 10003
=> C. = 10104
=> D. = 10092
=> E. = 10164
Since the numbers are divisible by 21 => they are divisible by 3
=> Sum of the digits should be divisible by 3
(Watch this video to MASTER DIVISIBILITYRULES)
=> A. Sum of digits = 1+0+1+5+4 = 11 NOT DIVISIBLE by 3 =>ELIMINATE
=> B. Sum of digits = 1+0+0+0+3 = 4 NOT DIVISIBLE by 3 =>ELIMINATE
=> C. Sum of digits = 1+0+1+0+4 = 6 DIVISIBLE by 3 =>KEEP
=> D. Sum of digits = 1+0+0+9+2 = 12 DIVISIBLE by 3 =>KEEP
=> E. Sum of digits = 1+0+1+6+4 = 12 IVISIBLE by 3 =>[color=#27ae60]
...
Statistics : Posted by BrushMyQuant • on Jan 12, 2022 4:45 pm • Replies 3 • Views 1170
]]>
Iframe
What is the smallest five-digit number which when divided by 7, 11 and 21 leaves a remainder of 5 in eachcase?
Let's solve the problem using twomethods
Method 1:Elimination
Let's subtract 5 from all the option choices so that we have numbers which are divisible by 7, 11 and 21
=> A. = 10154 (10159-4)
=> B. = 10003
=> C. = 10104
=> D. = 10092
=> E. = 10164
Since the numbers are divisible by 21 => they are divisible by 3
=> Sum of the digits should be divisible by 3
(Watch this video to MASTER DIVISIBILITYRULES)
=> A. Sum of digits = 1+0+1+5+4 = 11 NOT DIVISIBLE by 3 =>ELIMINATE
=> B. Sum of digits = 1+0+0+0+3 = 4 NOT DIVISIBLE by 3 =>ELIMINATE
=> C. Sum of digits = 1+0+1+0+4 = 6 DIVISIBLE by 3 =>KEEP
=> D. Sum of digits = 1+0+0+9+2 = 12 DIVISIBLE by 3 =>KEEP
=> E. Sum of digits = 1+0+1+6+4 = 12 IVISIBLE by 3 =>[color=#27ae60]
...]]>
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Statistics : Posted by bumpbot • on Nov 05, 2018 8:22 am • Replies 4 • Views 1241
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Statistics : Posted by bumpbot • on Feb 06, 2012 1:20 am • Replies 16 • Views 8721
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Statistics : Posted by bumpbot • on Jun 11, 2013 11:31 am • Replies 18 • Views 15848
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Statistics : Posted by bumpbot • on Feb 10, 2017 4:42 pm • Replies 14 • Views 6587
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Statistics : Posted by bumpbot • on Jun 17, 2014 11:45 am • Replies 29 • Views 12488
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Statistics : Posted by bumpbot • on Jun 25, 2015 8:11 am • Replies 7 • Views 9502
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Statistics : Posted by bumpbot • on Jan 23, 2020 9:14 am • Replies 4 • Views 2960
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Statistics : Posted by bumpbot • on Feb 08, 2016 4:02 pm • Replies 13 • Views 10935
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Statistics : Posted by bumpbot • on May 22, 2020 3:33 pm • Replies 5 • Views 10033
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Statistics : Posted by bumpbot • on Jun 17, 2019 8:09 am • Replies 6 • Views 2099
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Statistics : Posted by bumpbot • on Jun 18, 2019 7:18 am • Replies 7 • Views 1264
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Statistics : Posted by bumpbot • on Feb 03, 2023 3:00 pm • Replies 3 • Views 1073
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How is B not an answer here? It directly weakens --> STOP imports from Qatania. So what if they are gas exporters themselves? It doesn't mean they dont import fromQantania.
Hi. You are not incorrect in your assumption. However, For B answer choice to work, you have to have multiple assumptions. GMAT CR does not like multiple assumptions (one is OK). It has to be a direct cause and effect.
With B, you have to have the following assumptions (which are unknown) and therefore this is the reason this cannot be the correctanswer:
- We have to assume that the gas exporing neighbors have imported meaningful amoung of gas in thepast and their change will reduce those exports. The need to import gas by gas exporters is doubtful but it could be true - you are notincorrect
- We have to assume that other export options such as shipping, LNG, and other export routes cannot handle thedelta of neighbors not importing additionalgas
- Andfinally, We have to assume that the reinvestment
...Statistics : Posted by bb • on Aug 15, 2022 1:03 pm • Replies 3 • Views 447
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How is B not an answer here? It directly weakens --> STOP imports from Qatania. So what if they are gas exporters themselves? It doesn't mean they dont import fromQantania.
Hi. You are not incorrect in your assumption. However, For B answer choice to work, you have to have multiple assumptions. GMAT CR does not like multiple assumptions (one is OK). It has to be a direct cause and effect.
With B, you have to have the following assumptions (which are unknown) and therefore this is the reason this cannot be the correctanswer:
- We have to assume that the gas exporing neighbors have imported meaningful amoung of gas in thepast and their change will reduce those exports. The need to import gas by gas exporters is doubtful but it could be true - you are notincorrect
- We have to assume that other export options such as shipping, LNG, and other export routes cannot handle thedelta of neighbors not importing additionalgas
- Andfinally, We have to assume that the reinvestment
...]]>
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Statistics : Posted by bumpbot • on Aug 03, 2015 5:25 pm • Replies 4 • Views 21379
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Statistics : Posted by bumpbot • on May 09, 2022 12:15 pm • Replies 7 • Views 1613
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Harmonic Progression is rarely ever tested on GMAT, atleast I’ve not seen in over 2 years
It is not tested. You do not need to know the concept of harmonic mean Based on the questions I have seen.
I stand corrected. Apparently the new gym has focus does test harmonic mean 🥴
the-harmonic-mean-of-n-numbers-is-the-reciprocal-of-the-arithmetic-416989.html
I stand corrected. GMAT focus tests harmonic mean - above is an example from GMAT prep.
As was pointed out, I also have not seen it brought up much in the past.
Statistics : Posted by bb • on Oct 21, 2022 3:57 am • Replies 4491 • Views 130122
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Harmonic Progression is rarely ever tested on GMAT, atleast I’ve not seen in over 2 years
It is not tested. You do not need to know the concept of harmonic mean Based on the questions I have seen.
I stand corrected. Apparently the new gym has focus does test harmonic mean 🥴
the-harmonic-mean-of-n-numbers-is-the-reciprocal-of-the-arithmetic-416989.html
I stand corrected. GMAT focus tests harmonic mean - above is an example from GMAT prep.
As was pointed out, I also have not seen it brought up much in the past.]]>
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Statistics : Posted by bumpbot • on Jun 12, 2013 3:11 pm • Replies 15 • Views 23629
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Statistics : Posted by bumpbot • on Apr 12, 2018 4:31 am • Replies 13 • Views 6353
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Statistics : Posted by bumpbot • on Dec 19, 2018 8:10 am • Replies 2 • Views 2848
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But G will always be ahead of L ,hence divide it by 2 . Hence the ans is 120/2 = 60
MartyMurray KarishmaB
Statistics : Posted by sayan640 • on Jan 30, 2017 7:34 am • Replies 10 • Views 10979
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But G will always be ahead of L ,hence divide it by 2 . Hence the ans is 120/2 = 60
MartyMurray KarishmaB]]>
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Statistics : Posted by bumpbot • on Aug 21, 2019 6:02 am • Replies 6 • Views 2987
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not understanding why
Posted from my mobile device
Statistics : Posted by Sa800 • on Apr 25, 2017 7:28 am • Replies 7 • Views 4838
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not understanding why
Posted from my mobile device]]>
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Statistics : Posted by bumpbot • on Mar 16, 2020 6:52 pm • Replies 5 • Views 6110
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Statistics : Posted by bumpbot • on Mar 03, 2017 6:24 pm • Replies 9 • Views 12202
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A box contains 10 pairs of shoes (20 shoes in total). If two shoes are selected at random, what it is the probability that they are matching shoes?
A. 1/190
B. 1/20
C. 1/19
D. 1/10
E. 1/9
There are basically 10 pairs, and we need to pick a pair of shoes, why is the answer simply not 1/10?
Statistics : Posted by nisheshj • on Oct 28, 2009 8:08 am • Replies 22 • Views 69294
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A box contains 10 pairs of shoes (20 shoes in total). If two shoes are selected at random, what it is the probability that they are matching shoes?
A. 1/190
B. 1/20
C. 1/19
D. 1/10
E. 1/9
There are basically 10 pairs, and we need to pick a pair of shoes, why is the answer simply not 1/10?]]>
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Statistics : Posted by bumpbot • on Jun 17, 2019 8:19 am • Replies 10 • Views 8999
]]>
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Statistics : Posted by bumpbot • on Mar 06, 2019 6:14 am • Replies 3 • Views 2347
]]>
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Statistics : Posted by bumpbot • on Mar 21, 2017 12:10 pm • Replies 15 • Views 5855
]]>
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Statistics : Posted by bumpbot • on Jul 13, 2011 5:20 am • Replies 13 • Views 13524
]]>
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Algebraically, this is time consuming. Finding the roots of the equation, checking the values and then plugging in the value of x in the final equation is not the ideal method to approach the question, in my opinion.
BTW, the answer is C.
Statistics : Posted by saswat1987 • on Apr 23, 2024 8:30 am • Replies 6 • Views 335
]]>
Algebraically, this is time consuming. Finding the roots of the equation, checking the values and then plugging in the value of x in the final equation is not the ideal method to approach the question, in my opinion.
BTW, the answer is C.]]>
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Statistics : Posted by bumpbot • on Feb 05, 2019 9:14 am • Replies 4 • Views 2961
]]>
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https://gmatclub.com/forum/m41-429061.html
Statistics : Posted by Bunuel • on Oct 25, 2021 6:00 pm • Replies 2 • Views 601
]]>
https://gmatclub.com/forum/m41-429061.html]]>
If\(x\) and\(y\) are integers and\( ((x - 1)(y - 1))! =2\) , which of the following could be a value of\(xy\) ?
I. -6
II. 0
III. 6
A. I only
B. II only
C. II only
D. II and III only
E. I, II, and III
Only\( 2! =2\) , so we have that\( (x - 1)(y - 1) =2\) .
Since\(x\) and\(y\) are integers, we can have the following four cases:
\( (x -1)=2\) and\( (y - 1) =1\) . This gives\(x=3\) and\(y=2\) .
\( (x -1)=1\) and\( (y - 1) =2\) . This gives\(x=2\) and\(y=3\) .
\( (x -1)=-2\) and\( (y - 1) =-1\) . This gives\(x=-1\) and\(y=0\) .
\( (x -1)=-1\) and\( (y - 1) =-2\) . This gives\(x=0\) and\(y=-1\) .
The first two cases yield\(xy=6\) , and the last two cases yield\(xy=0\) .
Answer: D
...
Statistics : Posted by Bunuel • on Apr 26, 2024 3:10 pm • Replies 1 • Views 35
]]>
If\(x\) and\(y\) are integers and\( ((x - 1)(y - 1))! =2\) , which of the following could be a value of\(xy\) ?
I. -6
II. 0
III. 6
A. I only
B. II only
C. II only
D. II and III only
E. I, II, and III
Only\( 2! =2\) , so we have that\( (x - 1)(y - 1) =2\) .
Since\(x\) and\(y\) are integers, we can have the following four cases:
\( (x -1)=2\) and\( (y - 1) =1\) . This gives\(x=3\) and\(y=2\) .
\( (x -1)=1\) and\( (y - 1) =2\) . This gives\(x=2\) and\(y=3\) .
\( (x -1)=-2\) and\( (y - 1) =-1\) . This gives\(x=-1\) and\(y=0\) .
\( (x -1)=-1\) and\( (y - 1) =-2\) . This gives\(x=0\) and\(y=-1\) .
The first two cases yield\(xy=6\) , and the last two cases yield\(xy=0\) .
Answer: D
...]]>
https://gmatclub.com/forum/m41-429059.html
Statistics : Posted by Bunuel • on Oct 18, 2021 6:08 pm • Replies 2 • Views 501
]]>
https://gmatclub.com/forum/m41-429059.html]]>
If \(n\) is a positive two-digit integer and \(nx = x!\), what is the value of the positive integer \(x\)?
A. 2
B. 3
C. 4
D. 5
E. 24
Given that \(x! = (x - 1)!* x\), we have: \(nx = (x - 1)! * x\).
Reducing the above by \(x\) gives \(n = (x - 1)! \)
Given that \(n\) is a positive two-digit integer, then \(n\) equals 24 (recall that 3! = 6, 4! = 24, and 5! = 120, so only 24 is a two-digit integer equal to a factorial of a number). Thus, \((x - 1)! = 24\), which gives \(x - 1 = 4\), and finally \(x = 5\).
Answer: D
Statistics : Posted by Bunuel • on Apr 26, 2024 2:48 pm • Replies 1 • Views 23
]]>
If \(n\) is a positive two-digit integer and \(nx = x!\), what is the value of the positive integer \(x\)?
A. 2
B. 3
C. 4
D. 5
E. 24
Given that \(x! = (x - 1)!* x\), we have: \(nx = (x - 1)! * x\).
Reducing the above by \(x\) gives \(n = (x - 1)! \)
Given that \(n\) is a positive two-digit integer, then \(n\) equals 24 (recall that 3! = 6, 4! = 24, and 5! = 120, so only 24 is a two-digit integer equal to a factorial of a number). Thus, \((x - 1)! = 24\), which gives \(x - 1 = 4\), and finally \(x = 5\).
Answer: D]]>
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Statistics : Posted by bumpbot • on May 07, 2014 1:34 pm • Replies 13 • Views 5976
]]>
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If\( |x| <x^2\) , which of the following must be true?
I.\( x^2 >1\)
II.\( x >0\)
III.\( x <-1\)
(A) I only
(B) II only
(C) III only
(D) I and II only
(E) I and IIIonly
PLEASE READ THE WHOLE THREAD AND FOLLOW THE LINKS PROVIDED IN ORDER TO UNDERSTAND THE QUESTION/SOLUTIONSCORRECTLY.
Bunuel KarishmaB MartyMurray
I did it this way by squaring both sides. Does it make sense? Thanks.
...
Statistics : Posted by Engineer1 • on Aug 20, 2010 7:59 pm • Replies 50 • Views 75924
]]>
If\( |x| <x^2\) , which of the following must be true?
I.\( x^2 >1\)
II.\( x >0\)
III.\( x <-1\)
(A) I only
(B) II only
(C) III only
(D) I and II only
(E) I and IIIonly
PLEASE READ THE WHOLE THREAD AND FOLLOW THE LINKS PROVIDED IN ORDER TO UNDERSTAND THE QUESTION/SOLUTIONSCORRECTLY.
Bunuel KarishmaB MartyMurray
I did it this way by squaring both sides. Does it make sense? Thanks.
...]]>
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Statistics : Posted by bumpbot • on Jun 23, 2016 4:59 pm • Replies 4 • Views 18232
]]>
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Statistics : Posted by bumpbot • on Sep 11, 2010 8:53 am • Replies 8 • Views 14015
]]>
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The difference is 0.006, therefore it will be 10x smaller than 6% or 3/50 * 1/10 = 3/500
Statistics : Posted by kokus • on Oct 30, 2018 7:14 am • Replies 5 • Views 5673
]]>
The difference is 0.006, therefore it will be 10x smaller than 6% or 3/50 * 1/10 = 3/500]]>
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Statistics : Posted by bumpbot • on Oct 31, 2012 5:49 am • Replies 13 • Views 8013
]]>
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Statistics : Posted by bumpbot • on Jun 28, 2018 5:29 am • Replies 9 • Views 2215
]]>
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Bunuel wrote:
No typo there. Would anyone else like to try?
Argg! Apologies for the oversight
.Edited my solution now :)
Statistics : Posted by gmatophobia • on Apr 26, 2024 8:30 am • Replies 4 • Views 192
]]>
Bunuel wrote:
No typo there. Would anyone else like to try?
Argg! Apologies for the oversight
.Edited my solution now :)]]>
A country is divided into exactly 4 regions. Miki is sketching a map of the country's regions and plans to choose a color scheme for her map in which each region will be exactly 1 of 3 different colors and no adjacent regions will be the same color. One possible color scheme is for Regions 1,3 and 4 to have the same color and Region 2 to have a different color. How many color schemes are possible for Mikis map?
A) 6
B) 8
C) 9
D) 24
E)36
Attachment:
M1.png
Region 2 is adjacent to all three regions, while the remaining regions are adjacent only to Region 2 and thus depend only on Region 2's color.
Region 2 can be painted in one of three colors. Then, each of the remaining regions can be painted in any of the two remaining colors, making the number of different schemes equal to 3 * 2 * 2 * 2 = 24.
Answer: D.
...
Statistics : Posted by Bunuel • on Nov 06, 2023 7:25 am • Replies 5 • Views 2306
]]>
A country is divided into exactly 4 regions. Miki is sketching a map of the country's regions and plans to choose a color scheme for her map in which each region will be exactly 1 of 3 different colors and no adjacent regions will be the same color. One possible color scheme is for Regions 1,3 and 4 to have the same color and Region 2 to have a different color. How many color schemes are possible for Mikis map?
A) 6
B) 8
C) 9
D) 24
E)36
Attachment:
M1.png
Region 2 is adjacent to all three regions, while the remaining regions are adjacent only to Region 2 and thus depend only on Region 2's color.
Region 2 can be painted in one of three colors. Then, each of the remaining regions can be painted in any of the two remaining colors, making the number of different schemes equal to 3 * 2 * 2 * 2 = 24.
Answer: D.
...]]>