GMAT Club Forum - Forums > Problem Solving (PS) https://gmatclub.com:443/forum/index.php Join the largest GMAT and MBA community at GMAT Club. Get expert advice, free tests, questions and admission tips. Boost your GMAT score and MBA chances en-gb Copyright (c) 2002 GMAT Club Forum mail@gmatclub.com (GMAT Club Forum) mail@gmatclub.com (GMAT Club Forum) Sat, 27 Apr 2024 00:00:00 -0800 Sat, 27 Apr 2024 00:12:09 -0800 MSSTI RSS Feed 2.0 Version 1.0.9 - (C) 2008-2009 leviatan21 - http://www.mssti.com/ GMAT Club Forum - Forums > Problem Solving (PS) https://gmatclub.com:443/forum/tps://cdn.gmatclub.com/cdn/files/forum/styles/gmatclub_light/imageset/site_logo.gif https://gmatclub.com:443/forum/index.php 60 Problem Solving (PS) | Re: The cost of fuel increases by 10%. By what % must the consumption of https://gmatclub.com:443/forum/viewtopic.php?p=3389369#p3389369
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Statistics : Posted by bumpbot • on 07 Jul 2017, 02:10 • Replies 21 • Views 24993


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(bumpbot)Sat, 27 Apr 2024 00:00:22 -0800https://gmatclub.com:443/forum/viewtopic.php?p=3389369#p3389369
Problem Solving (PS) | Re: What is the smallest five-digit number which when divided by 7, 11 and https://gmatclub.com:443/forum/viewtopic.php?p=3389368#p3389368 ↧↧↧ 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 1154


]]>
↧↧↧ 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]
...]]>
(BrushMyQuant)Fri, 26 Apr 2024 23:56:40 -0800https://gmatclub.com:443/forum/viewtopic.php?p=3389368#p3389368
Problem Solving (PS) | Re: If Steves original salary is increased by 5 percent and then, 3 month https://gmatclub.com:443/forum/viewtopic.php?p=3389367#p3389367
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(bumpbot)Fri, 26 Apr 2024 23:49:16 -0800https://gmatclub.com:443/forum/viewtopic.php?p=3389367#p3389367
Problem Solving (PS) | Re: Exactly 36% of the numbers in set S are even multiples of 3. https://gmatclub.com:443/forum/viewtopic.php?p=3389365#p3389365
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Statistics : Posted by bumpbot • on 05 Feb 2012, 18:20 • Replies 16 • Views 8711


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(bumpbot)Fri, 26 Apr 2024 23:35:33 -0800https://gmatclub.com:443/forum/viewtopic.php?p=3389365#p3389365
Problem Solving (PS) | Re: There are three different hoses used to fill a pool: hose https://gmatclub.com:443/forum/viewtopic.php?p=3389356#p3389356
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Statistics : Posted by bumpbot • on 11 Jun 2013, 04:31 • Replies 18 • Views 15842


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(bumpbot)Fri, 26 Apr 2024 22:44:09 -0800https://gmatclub.com:443/forum/viewtopic.php?p=3389356#p3389356
Problem Solving (PS) | Re: When positive integer x is divided by 20, the remainder is 8. What is https://gmatclub.com:443/forum/viewtopic.php?p=3389354#p3389354
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Statistics : Posted by bumpbot • on 10 Feb 2017, 09:42 • Replies 14 • Views 6583


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(bumpbot)Fri, 26 Apr 2024 22:34:06 -0800https://gmatclub.com:443/forum/viewtopic.php?p=3389354#p3389354
Problem Solving (PS) | Re: X takes 10 days to complete a task. Y takes half that time https://gmatclub.com:443/forum/viewtopic.php?p=3389352#p3389352
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Statistics : Posted by bumpbot • on 17 Jun 2014, 04:45 • Replies 29 • Views 12482


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(bumpbot)Fri, 26 Apr 2024 22:32:33 -0800https://gmatclub.com:443/forum/viewtopic.php?p=3389352#p3389352
Problem Solving (PS) | Re: When integer n is divided by 15, the remainder is 5. Which of the foll https://gmatclub.com:443/forum/viewtopic.php?p=3389348#p3389348
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Statistics : Posted by bumpbot • on 25 Jun 2015, 01:11 • Replies 7 • Views 9498


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(bumpbot)Fri, 26 Apr 2024 22:23:53 -0800https://gmatclub.com:443/forum/viewtopic.php?p=3389348#p3389348
Problem Solving (PS) | Re: The gravitational force between two objects, F, is given by the formul https://gmatclub.com:443/forum/viewtopic.php?p=3389344#p3389344
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Statistics : Posted by bumpbot • on 23 Jan 2020, 02:14 • Replies 4 • Views 2953


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(bumpbot)Fri, 26 Apr 2024 21:50:31 -0800https://gmatclub.com:443/forum/viewtopic.php?p=3389344#p3389344
Problem Solving (PS) | Re: When positive integer k is divided by 6 the remainder is 3 https://gmatclub.com:443/forum/viewtopic.php?p=3389343#p3389343
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Statistics : Posted by bumpbot • on 08 Feb 2016, 09:02 • Replies 13 • Views 10926


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(bumpbot)Fri, 26 Apr 2024 21:48:46 -0800https://gmatclub.com:443/forum/viewtopic.php?p=3389343#p3389343
Problem Solving (PS) | Re: How many integers between 10 and 20, inclusive, have a remainder of 1 https://gmatclub.com:443/forum/viewtopic.php?p=3389341#p3389341
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Statistics : Posted by bumpbot • on 22 May 2020, 08:33 • Replies 5 • Views 10030


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(bumpbot)Fri, 26 Apr 2024 21:44:49 -0800https://gmatclub.com:443/forum/viewtopic.php?p=3389341#p3389341
Problem Solving (PS) | Re: If set Q consists of all three digit numbers divisible by 4, what is https://gmatclub.com:443/forum/viewtopic.php?p=3389335#p3389335
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Statistics : Posted by bumpbot • on 17 Jun 2019, 01:09 • Replies 6 • Views 2093


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(bumpbot)Fri, 26 Apr 2024 21:30:46 -0800https://gmatclub.com:443/forum/viewtopic.php?p=3389335#p3389335
Problem Solving (PS) | Re: Alex notices that a certain bacterium splits into 2 separate bacteria https://gmatclub.com:443/forum/viewtopic.php?p=3389334#p3389334
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Statistics : Posted by bumpbot • on 18 Jun 2019, 00:18 • Replies 7 • Views 1259


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(bumpbot)Fri, 26 Apr 2024 21:29:54 -0800https://gmatclub.com:443/forum/viewtopic.php?p=3389334#p3389334
Problem Solving (PS) | Re: The numbers in set P denote the distance of certain positive integers https://gmatclub.com:443/forum/viewtopic.php?p=3389333#p3389333
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Statistics : Posted by bumpbot • on 03 Feb 2023, 08:00 • Replies 3 • Views 1070


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(bumpbot)Fri, 26 Apr 2024 21:22:48 -0800https://gmatclub.com:443/forum/viewtopic.php?p=3389333#p3389333
Quantitative Questions | Re: ­­When it operates at its own constant rate, hose A can fill an empty https://gmatclub.com:443/forum/viewtopic.php?p=3389331#p3389331 Statistics : Posted by Danou • on 26 Apr 2024, 21:16 • Replies 1 • Views 34


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(Danou)Fri, 26 Apr 2024 21:16:44 -0800https://gmatclub.com:443/forum/viewtopic.php?p=3389331#p3389331
GMAT Club Tests | Re: V36-11 https://gmatclub.com:443/forum/viewtopic.php?p=3389313#p3389313 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: 
  1. 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
  2. We have to assume that other export options such as shipping, LNG, and other export routes cannot handle thedelta of neighbors not importing additionalgas
  3. Andfinally,  We have to assume that the reinvestment
    ...

    Statistics : Posted by bb • on 15 Aug 2022, 06:03 • Replies 3 • Views 445


    ]]> 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: 
    1. 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
    2. We have to assume that other export options such as shipping, LNG, and other export routes cannot handle thedelta of neighbors not importing additionalgas
    3. Andfinally,  We have to assume that the reinvestment
      ...]]> (bb)Fri, 26 Apr 2024 19:34:05 -0800https://gmatclub.com:443/forum/viewtopic.php?p=3389313#p3389313 GMAT Club Tests | Re: V08-02 https://gmatclub.com:443/forum/viewtopic.php?p=3389312#p3389312
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      Statistics : Posted by bumpbot • on 03 Aug 2015, 10:25 • Replies 4 • Views 21378


      ]]>

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      (bumpbot)Fri, 26 Apr 2024 19:28:54 -0800https://gmatclub.com:443/forum/viewtopic.php?p=3389312#p3389312
      Problem Solving (PS) | Re: Three numbers are in the ratio 3:4:5. The sum of the largest and the https://gmatclub.com:443/forum/viewtopic.php?p=3389310#p3389310
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      Statistics : Posted by bumpbot • on 09 May 2022, 05:15 • Replies 7 • Views 1611


      ]]>

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      (bumpbot)Fri, 26 Apr 2024 19:16:24 -0800https://gmatclub.com:443/forum/viewtopic.php?p=3389310#p3389310
      Quantitative Questions | Re: Quant Question of the Day Chat https://gmatclub.com:443/forum/viewtopic.php?p=3389307#p3389307 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 130101


      ]]>
      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.]]>
      (bb)Fri, 26 Apr 2024 17:36:01 -0800https://gmatclub.com:443/forum/viewtopic.php?p=3389307#p3389307
      Problem Solving (PS) | Re: Let p = the product of all the odd integers between 500 and https://gmatclub.com:443/forum/viewtopic.php?p=3389306#p3389306
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      Statistics : Posted by bumpbot • on 12 Jun 2013, 08:11 • Replies 15 • Views 23628


      ]]>

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      (bumpbot)Fri, 26 Apr 2024 17:10:03 -0800https://gmatclub.com:443/forum/viewtopic.php?p=3389306#p3389306
      Problem Solving (PS) | Re: If four integers, a, b, c, and d are chosen at random with replacement https://gmatclub.com:443/forum/viewtopic.php?p=3389304#p3389304
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      Statistics : Posted by bumpbot • on 11 Apr 2018, 21:31 • Replies 13 • Views 6353


      ]]>

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      (bumpbot)Fri, 26 Apr 2024 17:04:39 -0800https://gmatclub.com:443/forum/viewtopic.php?p=3389304#p3389304
      Problem Solving (PS) | Re: Two trains starting from cities 300 miles apart head toward each other https://gmatclub.com:443/forum/viewtopic.php?p=3389302#p3389302
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      Statistics : Posted by bumpbot • on 19 Dec 2018, 01:10 • Replies 2 • Views 2848


      ]]>

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      (bumpbot)Fri, 26 Apr 2024 16:27:27 -0800https://gmatclub.com:443/forum/viewtopic.php?p=3389302#p3389302
      Problem Solving (PS) | How many 4-letter words can be formed using the alphabets of the word https://gmatclub.com:443/forum/viewtopic.php?p=3389301#p3389301 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 10976


      ]]>
      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]]>
      (sayan640)Fri, 26 Apr 2024 16:14:01 -0800https://gmatclub.com:443/forum/viewtopic.php?p=3389301#p3389301
      Problem Solving (PS) | Re: The mean weight of 12 packages a retailer needs to ship on Monday is 1 https://gmatclub.com:443/forum/viewtopic.php?p=3389297#p3389297
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      Statistics : Posted by bumpbot • on 20 Aug 2019, 23:02 • Replies 6 • Views 2985


      ]]>

      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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      (bumpbot)Fri, 26 Apr 2024 15:33:06 -0800https://gmatclub.com:443/forum/viewtopic.php?p=3389297#p3389297
      Problem Solving (PS) | Re: 50% of students study science and 30% of science students score https://gmatclub.com:443/forum/viewtopic.php?p=3389294#p3389294
      not understanding why

      Posted from my mobile device

      Attachments IMG_0304.jpeg
      IMG_0304.jpeg [ 1022.13 KiB | Viewed 67 times ]

      Statistics : Posted by Sa800 • on 25 Apr 2017, 00:28 • Replies 7 • Views 4836


      ]]>

      not understanding why

      Posted from my mobile device

      Attachments IMG_0304.jpeg
      IMG_0304.jpeg [ 1022.13 KiB | Viewed 67 times ]
      ]]>
      (Sa800)Fri, 26 Apr 2024 14:39:45 -0800https://gmatclub.com:443/forum/viewtopic.php?p=3389294#p3389294
      Problem Solving (PS) | Re: What is the highest power of 5 that will divide https://gmatclub.com:443/forum/viewtopic.php?p=3389275#p3389275
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      Statistics : Posted by bumpbot • on 16 Mar 2020, 11:52 • Replies 5 • Views 6103


      ]]>

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      (bumpbot)Fri, 26 Apr 2024 13:21:18 -0800https://gmatclub.com:443/forum/viewtopic.php?p=3389275#p3389275
      Problem Solving (PS) | Re: At the Zamenhof Language School, at least 70% of the students take Eng https://gmatclub.com:443/forum/viewtopic.php?p=3389267#p3389267
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      Statistics : Posted by bumpbot • on 03 Mar 2017, 11:24 • Replies 9 • Views 12200


      ]]>

      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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      (bumpbot)Fri, 26 Apr 2024 12:06:27 -0800https://gmatclub.com:443/forum/viewtopic.php?p=3389267#p3389267
      Problem Solving (PS) | Re: A box contains 10 pairs of shoes (20 shoes in total). If two https://gmatclub.com:443/forum/viewtopic.php?p=3389246#p3389246 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 69292


      ]]>
      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?]]>
      (nisheshj)Fri, 26 Apr 2024 11:04:51 -0800https://gmatclub.com:443/forum/viewtopic.php?p=3389246#p3389246
      Problem Solving (PS) | Re: A folk group wants to have one concert on each of the seven consecutiv https://gmatclub.com:443/forum/viewtopic.php?p=3389238#p3389238
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      Statistics : Posted by bumpbot • on 17 Jun 2019, 01:19 • Replies 10 • Views 8995


      ]]>

      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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      (bumpbot)Fri, 26 Apr 2024 10:40:23 -0800https://gmatclub.com:443/forum/viewtopic.php?p=3389238#p3389238
      Problem Solving (PS) | Re: If 0 < x^y < 1, which of the following must be greater than x? https://gmatclub.com:443/forum/viewtopic.php?p=3389211#p3389211
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      Statistics : Posted by bumpbot • on 05 Mar 2019, 23:14 • Replies 3 • Views 2345


      ]]>

      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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      (bumpbot)Fri, 26 Apr 2024 09:27:55 -0800https://gmatclub.com:443/forum/viewtopic.php?p=3389211#p3389211
      Problem Solving (PS) | Re: In her position as a real estate agent, Sarah receives a bonus for eac https://gmatclub.com:443/forum/viewtopic.php?p=3389210#p3389210
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      Statistics : Posted by bumpbot • on 21 Mar 2017, 05:10 • Replies 15 • Views 5847


      ]]>

      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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      (bumpbot)Fri, 26 Apr 2024 09:26:22 -0800https://gmatclub.com:443/forum/viewtopic.php?p=3389210#p3389210
      Problem Solving (PS) | Re: How many positive integers less than 5,000 are evenly divisi https://gmatclub.com:443/forum/viewtopic.php?p=3389209#p3389209
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      Statistics : Posted by bumpbot • on 12 Jul 2011, 22:20 • Replies 13 • Views 13522


      ]]>

      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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      (bumpbot)Fri, 26 Apr 2024 09:25:40 -0800https://gmatclub.com:443/forum/viewtopic.php?p=3389209#p3389209
      Problem Solving (PS) | Re: If x is a non-zero integer and |x^2 - 2| - |x - 2| = -2, what is the https://gmatclub.com:443/forum/viewtopic.php?p=3389208#p3389208 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 335


      ]]> 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.­]]>
      (saswat1987)Fri, 26 Apr 2024 09:25:07 -0800https://gmatclub.com:443/forum/viewtopic.php?p=3389208#p3389208 Problem Solving (PS) | Re: What is the probability that the sum of two different single-digit pri https://gmatclub.com:443/forum/viewtopic.php?p=3389201#p3389201
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      Statistics : Posted by bumpbot • on 05 Feb 2019, 02:14 • Replies 4 • Views 2959


      ]]>

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      (bumpbot)Fri, 26 Apr 2024 08:51:40 -0800https://gmatclub.com:443/forum/viewtopic.php?p=3389201#p3389201
      GMAT Club Tests | Re: M36-44 https://gmatclub.com:443/forum/viewtopic.php?p=3389185#p3389185
      https://gmatclub.com/forum/m41-429061.html

      Statistics : Posted by Bunuel • on 25 Oct 2021, 11:00 • Replies 2 • Views 600


      ]]>

      https://gmatclub.com/forum/m41-429061.html]]>
      (Bunuel)Fri, 26 Apr 2024 08:13:08 -0800https://gmatclub.com:443/forum/viewtopic.php?p=3389185#p3389185
      GMAT Club Tests | Re M41-09 https://gmatclub.com:443/forum/viewtopic.php?p=3389181#p3389181 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 35


      ]]>
      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
      ...]]>
      (Bunuel)Fri, 26 Apr 2024 08:10:36 -0800https://gmatclub.com:443/forum/viewtopic.php?p=3389181#p3389181
      GMAT Club Tests | Re: M36-39 https://gmatclub.com:443/forum/viewtopic.php?p=3389173#p3389173
      https://gmatclub.com/forum/m41-429059.html

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


      ]]>

      https://gmatclub.com/forum/m41-429059.html]]>
      (Bunuel)Fri, 26 Apr 2024 07:53:45 -0800https://gmatclub.com:443/forum/viewtopic.php?p=3389173#p3389173
      GMAT Club Tests | Re M41-08 https://gmatclub.com:443/forum/viewtopic.php?p=3389169#p3389169 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


      ]]>
      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]]>
      (Bunuel)Fri, 26 Apr 2024 07:48:23 -0800https://gmatclub.com:443/forum/viewtopic.php?p=3389169#p3389169
      Problem Solving (PS) | Re: Jack purchased two chairs at a discount of 50% https://gmatclub.com:443/forum/viewtopic.php?p=3389164#p3389164
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      Statistics : Posted by bumpbot • on 07 May 2014, 06:34 • Replies 13 • Views 5973


      ]]>

      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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      (bumpbot)Fri, 26 Apr 2024 07:36:50 -0800https://gmatclub.com:443/forum/viewtopic.php?p=3389164#p3389164
      Problem Solving (PS) | Re: If |x| < x^2, which of the following must be true? https://gmatclub.com:443/forum/viewtopic.php?p=3389157#p3389157 mehdiov wrote:

      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.
      ...

      Attachments image0 (11).jpeg
      image0 (11).jpeg [ 2.23 MiB | Viewed 47 times ]

      Statistics : Posted by Engineer1 • on 20 Aug 2010, 12:59 • Replies 50 • Views 75915


      ]]>
      mehdiov wrote:

      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.
      ...

      Attachments image0 (11).jpeg
      image0 (11).jpeg [ 2.23 MiB | Viewed 47 times ]
      ]]>
      (Engineer1)Fri, 26 Apr 2024 07:28:31 -0800https://gmatclub.com:443/forum/viewtopic.php?p=3389157#p3389157
      Problem Solving (PS) | Re: The chart above shows year-end values for Darnella's investments. For https://gmatclub.com:443/forum/viewtopic.php?p=3389135#p3389135
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      Statistics : Posted by bumpbot • on 23 Jun 2016, 09:59 • Replies 4 • Views 18229


      ]]>

      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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      (bumpbot)Fri, 26 Apr 2024 06:25:17 -0800https://gmatclub.com:443/forum/viewtopic.php?p=3389135#p3389135
      Problem Solving (PS) | Re: When the integer k is divided by 12, the remainder is 3. Whi https://gmatclub.com:443/forum/viewtopic.php?p=3389134#p3389134
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      Statistics : Posted by bumpbot • on 11 Sep 2010, 01:53 • Replies 8 • Views 14014


      ]]>

      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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      (bumpbot)Fri, 26 Apr 2024 06:18:21 -0800https://gmatclub.com:443/forum/viewtopic.php?p=3389134#p3389134
      Problem Solving (PS) | Re: The number 0.756 is how much greater than 3/4? https://gmatclub.com:443/forum/viewtopic.php?p=3389130#p3389130
      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 30 Oct 2018, 00:14 • Replies 5 • Views 5673


      ]]>

      The difference is 0.006, therefore it will be 10x smaller than 6% or 3/50 * 1/10 = 3/500]]>
      (kokus)Fri, 26 Apr 2024 06:12:10 -0800https://gmatclub.com:443/forum/viewtopic.php?p=3389130#p3389130
      Problem Solving (PS) | Re: After the price of chocolates was discounted by 40%, a https://gmatclub.com:443/forum/viewtopic.php?p=3389127#p3389127
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      Statistics : Posted by bumpbot • on 30 Oct 2012, 22:49 • Replies 13 • Views 8009


      ]]>

      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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      (bumpbot)Fri, 26 Apr 2024 06:08:12 -0800https://gmatclub.com:443/forum/viewtopic.php?p=3389127#p3389127
      Problem Solving (PS) | Re: If ((14!)^25 - (14!)^11)/((14!)^11 - (14!)^4) = X. What is the unit di https://gmatclub.com:443/forum/viewtopic.php?p=3389119#p3389119
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      Statistics : Posted by bumpbot • on 27 Jun 2018, 22:29 • Replies 9 • Views 2211


      ]]>

      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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      (bumpbot)Fri, 26 Apr 2024 05:52:04 -0800https://gmatclub.com:443/forum/viewtopic.php?p=3389119#p3389119
      Problem Solving (PS) | If |y + 5| < 1 - x and x is a non-zero integer, what is the value of https://gmatclub.com:443/forum/viewtopic.php?p=3389118#p3389118
      Bunuel wrote:

      No typo there. Would anyone else like to try?­

      Argg! Apologies for the oversight   Image.

      Edited my solution now :)­

      Statistics : Posted by gmatophobia • on 26 Apr 2024, 01:30 • Replies 4 • Views 188


      ]]>
      Bunuel wrote:

      No typo there. Would anyone else like to try?­

      Argg! Apologies for the oversight   Image.

      Edited my solution now :)­]]>
      (gmatophobia)Fri, 26 Apr 2024 05:51:51 -0800https://gmatclub.com:443/forum/viewtopic.php?p=3389118#p3389118
      Problem Solving (PS) | Re: A country is divided into exactly 4 regions. Miki is sketching a map https://gmatclub.com:443/forum/viewtopic.php?p=3389112#p3389112 SN9633 wrote:

      Image
      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 06 Nov 2023, 00:25 • Replies 5 • Views 2304


      ]]>
      SN9633 wrote:

      Image
      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.
      ...]]>
      (Bunuel)Fri, 26 Apr 2024 05:40:40 -0800https://gmatclub.com:443/forum/viewtopic.php?p=3389112#p3389112
      Problem Solving (PS) | Re: If x£y represents the number of integers greater than x and less than https://gmatclub.com:443/forum/viewtopic.php?p=3389109#p3389109 RajibDhara wrote:

      Bunuel wrote:
      If x£y represents the number of integers greater than x and less than y, what is the value of –π£2?

      A) 2

      B) 3

      C) 4

      D) 5

      E) 6

      ­In GMAT FE, do we suppose to know n=pie, or they will provide info regarding the symbols that they provide and another problem i face in gmat club question bank there was a sum that said to convert foot to yard and no measure where given like 1 foot= somthing of yard which is usually given in gmat focus edition i guess and if it does not do we need to study measures as well ?

      ­It's not n, it's π there. Edited to avoided confusion.

      P.S. All relevant conversions will be provided in the prompt.

      Statistics : Posted by Bunuel • on 11 Jan 2019, 00:22 • Replies 5 • Views 4424


      ]]>
      RajibDhara wrote:

      Bunuel wrote:
      If x£y represents the number of integers greater than x and less than y, what is the value of –π£2?

      A) 2

      B) 3

      C) 4

      D) 5

      E) 6

      ­In GMAT FE, do we suppose to know n=pie, or they will provide info regarding the symbols that they provide and another problem i face in gmat club question bank there was a sum that said to convert foot to yard and no measure where given like 1 foot= somthing of yard which is usually given in gmat focus edition i guess and if it does not do we need to study measures as well ?

      ­It's not n, it's π there. Edited to avoided confusion.

      P.S. All relevant conversions will be provided in the prompt.]]>
      (Bunuel)Fri, 26 Apr 2024 05:31:49 -0800https://gmatclub.com:443/forum/viewtopic.php?p=3389109#p3389109
      Problem Solving (PS) | Re: If x is a non-negative integer and |6 - |x + 2|| = 10, then find the n https://gmatclub.com:443/forum/viewtopic.php?p=3389107#p3389107 Can,Will wrote:

      KarishmaB
      If p is a non-positive number, then for what value of p does the expression |77 – 6p| holds the minimum value?

      A. 77/12
      B. 77/6
      C. 12
      D. 0
      E. -77/6

      in this problem can we say that since p is a non positive I77-6pI is negative i.e -77+6p

      ­This question is discussed here:

      https://gmatclub.com/forum/if-x-is-a-no ... l#p3389087

      Statistics : Posted by Bunuel • on 07 May 2020, 09:29 • Replies 11 • Views 4551


      ]]>
      Can,Will wrote:

      KarishmaB
      If p is a non-positive number, then for what value of p does the expression |77 – 6p| holds the minimum value?

      A. 77/12
      B. 77/6
      C. 12
      D. 0
      E. -77/6

      in this problem can we say that since p is a non positive I77-6pI is negative i.e -77+6p

      ­This question is discussed here:

      https://gmatclub.com/forum/if-x-is-a-no ... l#p3389087]]>
      (Bunuel)Fri, 26 Apr 2024 05:23:30 -0800https://gmatclub.com:443/forum/viewtopic.php?p=3389107#p3389107
      Problem Solving (PS) | Re: The edge of a cube is measured as 100 centimeters. This Measurement https://gmatclub.com:443/forum/viewtopic.php?p=3389104#p3389104
      sayan640 wrote:

      KarishmaB Can you please help on this question ?
      SHould it not be 99*99*99 or 101*101*101 ? Not able to interpret it properly.gmatophobia MartyMurray

      ­Since you need maximum difference 101^3 is more appropriate but since you need an approximate, either will work just fine. 

      EstimatedVolume\( =100^3\)

      Max Actual Volume\( = 101^3 = (100 + 1)^3 = 100^3 +1 + 3*100 (100 +1)\) (Use (a+b)^3 formula)

      We need to find the extra (what is more than 100^3) so ignore the first term. Since we are approximating, ignore 1's. 30,000 is extra.

      Answer (B) 
      ...

      Statistics : Posted by KarishmaB • on 10 Jan 2024, 22:27 • Replies 9 • Views 1811


      ]]>
      sayan640 wrote:

      KarishmaB Can you please help on this question ?
      SHould it not be 99*99*99 or 101*101*101 ? Not able to interpret it properly.gmatophobia MartyMurray

      ­Since you need maximum difference 101^3 is more appropriate but since you need an approximate, either will work just fine. 

      EstimatedVolume\( =100^3\)

      Max Actual Volume\( = 101^3 = (100 + 1)^3 = 100^3 +1 + 3*100 (100 +1)\) (Use (a+b)^3 formula)

      We need to find the extra (what is more than 100^3) so ignore the first term. Since we are approximating, ignore 1's. 30,000 is extra.

      Answer (B) 
      ...]]>
      (KarishmaB)Fri, 26 Apr 2024 05:21:42 -0800https://gmatclub.com:443/forum/viewtopic.php?p=3389104#p3389104