GMAT Club Forum - Forums > Problem Solving (PS)

Problem Solving (PS) | Re: When it operates at its own constant rate, hose A can fill an empty

(Akkiiii) — Sat, 27 Apr 2024 03:47:07 -0800

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

Lets say Total 120 units
A fills in x hours
Speed of A= 12/x unit/hour

B fills in x/2 hours
Speed of B= 120*2/x= 240/x unit/ hour

Together Speed= 120/x+ 240/x= 360/x
Work= 120
Time= Work/Rate
120/ (360/x)= 120*x/360= 2x/3

A

Statistics : Posted by Akkiiii • on 26 Apr 2024, 21:16 • Replies 2 • Views 74

Problem Solving (PS) | Re: What is the maximum value of x, if |x|>x?

(RajibDhara) — Sat, 27 Apr 2024 03:42:10 -0800

chetan2u wrote:

What is the maximum value of integer x, if |x|>x?
(A) -10
(B) -1
(C) 0
(D) 10
(E) None of the above

Chetan's questions

x could be -0.1 as well and in that case none of the above will be correct, i guess the prompt should be add to mitigate such ambiguity. I got option B as answer but because of option E i got confuse.

Statistics : Posted by RajibDhara • on 31 Oct 2019, 07:03 • Replies 4 • Views 2786

Problem Solving (PS) | Re: If m and n are positive integers, and m + n and m/n are both even numb

(bumpbot) — Sat, 27 Apr 2024 02:58:50 -0800

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Statistics : Posted by bumpbot • on 28 Feb 2023, 12:30 • Replies 4 • Views 1987

Problem Solving (PS) | Re: If the sum of the square roots of two integers is

(bumpbot) — Sat, 27 Apr 2024 02:55:40 -0800

Statistics : Posted by bumpbot • on 30 Oct 2016, 07:36 • Replies 17 • Views 22487

Problem Solving (PS) | Re: 50% of students study science and 30% of science students score

(Bunuel) — Sat, 27 Apr 2024 02:29:12 -0800

Sa800 wrote:

50% of students’ study science and 30% of science students score more than 80% marks in the exam. If 40% of all students (science + non-science) get more than 80% marks in exam, what percentage of non-science students score less than 80% marks?

A. 30%
B. 40%
C. 50%
D. 60%
E. 70%

i get 40%

not understandingwhy

Posted from my mobiledevice

It seems that you missed the solutions above because each of the three shows the correct way of solving it. Here it isagain:

...

Statistics : Posted by Bunuel • on 25 Apr 2017, 00:28 • Replies 5 • Views 4871

Problem Solving (PS) | Re: Oneyde and Jorge must make two reservations for an airplane trip, in w

(bumpbot) — Sat, 27 Apr 2024 02:22:43 -0800

Statistics : Posted by bumpbot • on 01 Mar 2019, 09:07 • Replies 4 • Views 1040

Problem Solving (PS) | Re: In a sports club, 6 players are divided into 3 teams of 2 players. How

(bumpbot) — Sat, 27 Apr 2024 02:04:05 -0800

Statistics : Posted by bumpbot • on 04 Jan 2019, 01:18 • Replies 11 • Views 3897

Problem Solving (PS) | Re: There are 7 points on a straight line, L1, and another 8 points on

(bumpbot) — Sat, 27 Apr 2024 01:45:28 -0800

Statistics : Posted by bumpbot • on 25 Oct 2022, 01:22 • Replies 2 • Views 613

Problem Solving (PS) | Re: An artist has 3 hooks on the wall and 5 different pictures. How many d

(bumpbot) — Sat, 27 Apr 2024 01:41:48 -0800

Statistics : Posted by bumpbot • on 17 Nov 2022, 09:38 • Replies 5 • Views 1516

Problem Solving (PS) | Re: a is the product of 3 and the square root of 2, b is the product of 2

(bumpbot) — Sat, 27 Apr 2024 01:31:08 -0800

Statistics : Posted by bumpbot • on 16 Mar 2022, 03:15 • Replies 2 • Views 828

Problem Solving (PS) | Re: If (x^2)^(1/2)/(x^3)^(1/3) = -1and x 0, what is the value of

(Bunuel) — Sat, 27 Apr 2024 01:29:48 -0800

OokandGluk wrote:

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

\(\frac{\sqrt{x^2}}{\sqrt[3]{x^3}}\)

= \(\frac{|x|}{x}\)

\( \frac{|x|}{x} =-1\)

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 26 Apr 2024, 01:30 • Replies 4 • Views 210

Problem Solving (PS) | Re: The cost of fuel increases by 10%. By what % must the consumption of

(bumpbot) — Sat, 27 Apr 2024 00:00:22 -0800

Statistics : Posted by bumpbot • on 07 Jul 2017, 02:10 • Replies 21 • Views 25035

Problem Solving (PS) | Re: What is the smallest five-digit number which when divided by 7, 11 and

(BrushMyQuant) — Fri, 26 Apr 2024 23:56:40 -0800

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

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 12 Jan 2022, 09:45 • Replies 3 • Views 1177

Problem Solving (PS) | Re: If Steves original salary is increased by 5 percent and then, 3 month

(bumpbot) — Fri, 26 Apr 2024 23:49:16 -0800

Statistics : Posted by bumpbot • on 05 Nov 2018, 01:22 • Replies 4 • Views 1251

Problem Solving (PS) | Re: Exactly 36% of the numbers in set S are even multiples of 3.

(bumpbot) — Fri, 26 Apr 2024 23:35:33 -0800

Statistics : Posted by bumpbot • on 05 Feb 2012, 18:20 • Replies 16 • Views 8731

Problem Solving (PS) | Re: There are three different hoses used to fill a pool: hose

(bumpbot) — Fri, 26 Apr 2024 22:44:09 -0800

Statistics : Posted by bumpbot • on 11 Jun 2013, 04:31 • Replies 18 • Views 15854

Problem Solving (PS) | Re: When positive integer x is divided by 20, the remainder is 8. What is

(bumpbot) — Fri, 26 Apr 2024 22:34:06 -0800

Statistics : Posted by bumpbot • on 10 Feb 2017, 09:42 • Replies 14 • Views 6593

Problem Solving (PS) | Re: X takes 10 days to complete a task. Y takes half that time

(bumpbot) — Fri, 26 Apr 2024 22:32:33 -0800

Statistics : Posted by bumpbot • on 17 Jun 2014, 04:45 • Replies 29 • Views 12496

Problem Solving (PS) | Re: When integer n is divided by 15, the remainder is 5. Which of the foll

(bumpbot) — Fri, 26 Apr 2024 22:23:53 -0800

Statistics : Posted by bumpbot • on 25 Jun 2015, 01:11 • Replies 7 • Views 9504

Problem Solving (PS) | Re: The gravitational force between two objects, F, is given by the formul

(bumpbot) — Fri, 26 Apr 2024 21:50:31 -0800

Statistics : Posted by bumpbot • on 23 Jan 2020, 02:14 • Replies 4 • Views 2966

Problem Solving (PS) | Re: When positive integer k is divided by 6 the remainder is 3

(bumpbot) — Fri, 26 Apr 2024 21:48:46 -0800

Statistics : Posted by bumpbot • on 08 Feb 2016, 09:02 • Replies 13 • Views 10940

Problem Solving (PS) | Re: How many integers between 10 and 20, inclusive, have a remainder of 1

(bumpbot) — Fri, 26 Apr 2024 21:44:49 -0800

Statistics : Posted by bumpbot • on 22 May 2020, 08:33 • Replies 5 • Views 10038

Problem Solving (PS) | Re: If set Q consists of all three digit numbers divisible by 4, what is

(bumpbot) — Fri, 26 Apr 2024 21:30:46 -0800

Statistics : Posted by bumpbot • on 17 Jun 2019, 01:09 • Replies 6 • Views 2106

Problem Solving (PS) | Re: Alex notices that a certain bacterium splits into 2 separate bacteria

(bumpbot) — Fri, 26 Apr 2024 21:29:54 -0800

Statistics : Posted by bumpbot • on 18 Jun 2019, 00:18 • Replies 7 • Views 1266

Problem Solving (PS) | Re: The numbers in set P denote the distance of certain positive integers

(bumpbot) — Fri, 26 Apr 2024 21:22:48 -0800

Statistics : Posted by bumpbot • on 03 Feb 2023, 08:00 • Replies 3 • Views 1077

GMAT Club Tests | Re: V36-11

(bb) — Fri, 26 Apr 2024 19:34:05 -0800

unicornilove wrote:

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 15 Aug 2022, 06:03 • Replies 3 • Views 451

GMAT Club Tests | Re: V08-02

(bumpbot) — Fri, 26 Apr 2024 19:28:54 -0800

Statistics : Posted by bumpbot • on 03 Aug 2015, 10:25 • Replies 4 • Views 21379

Problem Solving (PS) | Re: Three numbers are in the ratio 3:4:5. The sum of the largest and the

(bumpbot) — Fri, 26 Apr 2024 19:16:24 -0800

Statistics : Posted by bumpbot • on 09 May 2022, 05:15 • Replies 7 • Views 1619

Quantitative Questions | Re: Quant Question of the Day Chat

(bb) — Fri, 26 Apr 2024 17:36:01 -0800

gmat_app1096 wrote:

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 20 Oct 2022, 20:57 • Replies 4491 • Views 130144

Problem Solving (PS) | Re: Let p = the product of all the odd integers between 500 and

(bumpbot) — Fri, 26 Apr 2024 17:10:03 -0800

Statistics : Posted by bumpbot • on 12 Jun 2013, 08:11 • Replies 15 • Views 23634

Problem Solving (PS) | Re: If four integers, a, b, c, and d are chosen at random with replacement

(bumpbot) — Fri, 26 Apr 2024 17:04:39 -0800

Statistics : Posted by bumpbot • on 11 Apr 2018, 21:31 • Replies 13 • Views 6365

Problem Solving (PS) | Re: Two trains starting from cities 300 miles apart head toward each other

(bumpbot) — Fri, 26 Apr 2024 16:27:27 -0800

Statistics : Posted by bumpbot • on 19 Dec 2018, 01:10 • Replies 2 • Views 2851

Problem Solving (PS) | Re: How many 4-letter words can be formed using the alphabets of the word

(sayan640) — Fri, 26 Apr 2024 16:14:01 -0800

With G and L thought as one entity , we can arrange the other two numbers in 5*4 ways i.e 20 ways.
For each of these ways , (GL) , _ , _ numbers can be arranged in 3! ways . Hence all the numbers can be arranged in 20 * 3! ways .
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 30 Jan 2017, 00:34 • Replies 10 • Views 10984

Problem Solving (PS) | Re: The mean weight of 12 packages a retailer needs to ship on Monday is 1

(bumpbot) — Fri, 26 Apr 2024 15:33:06 -0800

Statistics : Posted by bumpbot • on 20 Aug 2019, 23:02 • Replies 6 • Views 2993

Problem Solving (PS) | Re: What is the highest power of 5 that will divide

(bumpbot) — Fri, 26 Apr 2024 13:21:18 -0800

Statistics : Posted by bumpbot • on 16 Mar 2020, 11:52 • Replies 5 • Views 6115

Problem Solving (PS) | Re: At the Zamenhof Language School, at least 70% of the students take Eng

(bumpbot) — Fri, 26 Apr 2024 12:06:27 -0800

Statistics : Posted by bumpbot • on 03 Mar 2017, 11:24 • Replies 9 • Views 12205

Problem Solving (PS) | Re: A box contains 10 pairs of shoes (20 shoes in total). If two

(nisheshj) — Fri, 26 Apr 2024 11:04:51 -0800

tejal777 wrote:

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 28 Oct 2009, 01:08 • Replies 22 • Views 69296

Problem Solving (PS) | Re: A folk group wants to have one concert on each of the seven consecutiv

(bumpbot) — Fri, 26 Apr 2024 10:40:23 -0800

Statistics : Posted by bumpbot • on 17 Jun 2019, 01:19 • Replies 10 • Views 9006

Problem Solving (PS) | Re: If 0 < x^y < 1, which of the following must be greater than x?

(bumpbot) — Fri, 26 Apr 2024 09:27:55 -0800

Statistics : Posted by bumpbot • on 05 Mar 2019, 23:14 • Replies 3 • Views 2351

Problem Solving (PS) | Re: In her position as a real estate agent, Sarah receives a bonus for eac

(bumpbot) — Fri, 26 Apr 2024 09:26:22 -0800

Statistics : Posted by bumpbot • on 21 Mar 2017, 05:10 • Replies 15 • Views 5858

Problem Solving (PS) | Re: How many positive integers less than 5,000 are evenly divisi

(bumpbot) — Fri, 26 Apr 2024 09:25:40 -0800

Statistics : Posted by bumpbot • on 12 Jul 2011, 22:20 • Replies 13 • Views 13529

Problem Solving (PS) | Re: If x is a non-zero integer and |x^2 - 2| - |x - 2| = -2, what is the

(saswat1987) — Fri, 26 Apr 2024 09:25:07 -0800

Bunuel, Is there any other way of solving this question ?

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 23 Apr 2024, 01:30 • Replies 6 • Views 337

Problem Solving (PS) | Re: What is the probability that the sum of two different single-digit pri

(bumpbot) — Fri, 26 Apr 2024 08:51:40 -0800

Statistics : Posted by bumpbot • on 05 Feb 2019, 02:14 • Replies 4 • Views 2964

GMAT Club Tests | Re: M36-44

(Bunuel) — Fri, 26 Apr 2024 08:13:08 -0800

Similar PS question to practice:

https://gmatclub.com/forum/m41-429061.html

Statistics : Posted by Bunuel • on 25 Oct 2021, 11:00 • Replies 2 • Views 601

GMAT Club Tests | Re M41-09

(Bunuel) — Fri, 26 Apr 2024 08:10:36 -0800

OfficialSolution:

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 26 Apr 2024, 08:10 • Replies 1 • Views 36

GMAT Club Tests | Re: M36-39

(Bunuel) — Fri, 26 Apr 2024 07:53:45 -0800

Similar PS question to practice:

https://gmatclub.com/forum/m41-429059.html

Statistics : Posted by Bunuel • on 18 Oct 2021, 11:08 • Replies 2 • Views 501

GMAT Club Tests | Re M41-08

(Bunuel) — Fri, 26 Apr 2024 07:48:23 -0800

Official Solution:

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 26 Apr 2024, 07:48 • Replies 1 • Views 23

Problem Solving (PS) | Re: Jack purchased two chairs at a discount of 50%

(bumpbot) — Fri, 26 Apr 2024 07:36:50 -0800

Statistics : Posted by bumpbot • on 07 May 2014, 06:34 • Replies 13 • Views 5984

Problem Solving (PS) | Re: If |x| < x^2, which of the following must be true?

(Engineer1) — Fri, 26 Apr 2024 07:28:31 -0800

mehdiov wrote:

If\( |x|
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.
...

Attachments
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Statistics : Posted by Engineer1 • on 20 Aug 2010, 12:59 • Replies 50 • Views 75925

Problem Solving (PS) | Re: The chart above shows year-end values for Darnella's investments. For

(bumpbot) — Fri, 26 Apr 2024 06:25:17 -0800

Statistics : Posted by bumpbot • on 23 Jun 2016, 09:59 • Replies 4 • Views 18237