Problem Solving (PS) | Re: What is the product of all the solutions of (x + 2)^2 = |x + 2|?

March 11, 2024, 3:33 am

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unicornilove wrote:

HiBunuel , I followed this method and ended up with the same results but did -2*-1*-3*-2.

Question did not state distinct answers so 12 could be the answer aswell.

adewale223 wrote:

(x + 2 )^2 = /x + 2 /

x^2 + 4x + 4 = /x + 2 /

Case 1

When x + 2 is positive.

x^2 + 4x + 4 = x + 2

x^2 + 4x + 4 -x - 2 = 0

x^2 + 3x + 2 = 0

x = -2
x = -1

Case 2

When x + 2 is negative.

x^2 + 4x + 4 = -x - 2

x^2 + 5x + 6 = 0

x = -2

x = -3

Substituting the values shows x could be -1, -2, -3

Sum = -6

Answer choiceA

Firstly, the solutions of the equation are -1, -2, and -3. No one would say that the solutions are -1, -3, -2, AND -2 AGAIN.

Also, the method above lacks details to be 100% correct.

In case 1, when x + 2 is positive, it means the range is x > -2. So, you should discard x = -2, which you get for that case because it is not in the range.

In case 2, we should consider the scenario when x + 2 ≤ 0, giving the range x ≤ -2. Both x = -2 and x = -3 are in the range, so both are acceptable.

Thus,
...

Statistics : Posted by Bunuel • on 07 Aug 2023, 08:00 • Replies 12 • Views 8084

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Problem Solving (PS) | Re: Problem Solving Butler: 2 Questions Every Day

March 11, 2024, 3:37 am

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Problem Solving Butler: February 2023
March 11	PS 1	PS 2

Statistics : Posted by Bunuel • on 06 Nov 2018, 03:19 • Replies 12 • Views 121968

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Problem Solving (PS) | Which of the following is equivalent to 13 8 7x 85 ?

March 11, 2024, 3:53 am

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patriciachr wrote:

chetan2u wrote:

Bunuel wrote:

Which of the following is equivalent to$ –13 ≤ 8 – 7x ≤85$ ?

(A)$ |x + 4| ≤7$

(B)$ |x – 4| ≤7$

(C)$ |x + 11| ≥–3$

(D)$ |x – 36| ≤49$

(E)$ |x – 49| ≤36$

Simplify theinequality

$ –13 ≤ 8 – 7x ≤85$

$ -(85) ≤ -(8 – 7x) ≤-(-13)$

$ –85 ≤ 7x-8 ≤13$

$ –77 ≤ 7x ≤21$

$ –11 ≤ x ≤3$

Now, all options are of the type$ |x - a| ≤b$ , which is a-b ≤ x ≤ a+b

We can write$ –11 ≤ x ≤3$ as$ –4-7 ≤ x ≤-4+7$ . Thus, a=-4 andb=7
$ |x - a| ≤b$ =>$ |x -(-4)| ≤7$ =>$ |x +4)| ≤7$

A

OR

After simplifying to$ –11 ≤ x ≤3$ , we can also open the MOD in each option to get the answer.

(A)$ |x + 4| ≤7$
$ x + 4 ≤ 7........x\leq3$
$ -(x + 4 ≤ 7)........x\geq-11$
Exactly what we are lookingfor.

A

Understand that the midpoint is -4, but why does the answer become x+4?Thanks

$ –13 ≤ 8 – 7x ≤85$ is equivalentto $ –11 ≤ x ≤3$ .

Similarly, option A,$ |x + 4| ≤7$ , is equivalent to the sameexpression:
[indent]
...

Statistics : Posted by Bunuel • on 22 Feb 2022, 06:00 • Replies 5 • Views 4515

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Problem Solving (PS) | Re: A certain man can row a boat at 12 miles per hour in still water. If

March 11, 2024, 4:00 am

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GMAT Club Tests | Re: M23-06

March 11, 2024, 4:38 am

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Statistics : Posted by bumpbot • on 16 Sep 2014, 00:18 • Replies 4 • Views 17055

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Problem Solving (PS) | Re: A store sold 60 percent of the hats from a shipment of hats at a

March 11, 2024, 4:46 am

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unicornilove wrote:

Hi there,

Im trying to figure out where I went wrong and would appreciate if you could give me some help.
I have the same steps and calculations as you but start to go wrong when I calculate gross profit immediately for each selling price, 3c/2 and c/2.

Gross profit for 60% of hats = (3c/2-c)*0.6x = 0.3xc
Gross profit for 70% of remainder of hats = (c/2-c)*0.28x = -0.14xc

Total gross profit = 0.3xc -0.14xc = 0.16xc
Gross profit as % of total cost = 0.16xc / xc =16%.

GMATcpm wrote:

rakman123 wrote:

A store sold 60 percent of the hats from a shipment of hats at a selling price that was 50 percent greater than the store's cost for each hat. Then the store reduced the selling price by 66 2/3 percent and sold 70 percent of the remaining hats at the reduced selling price. If the store did not sell any other hats form the shipment, then the store's gross profit from the sale of the hats from the shipment was what percent of the store's cost for the hats from the shipment?

A) 1%
B)
...

Statistics : Posted by Bunuel • on 28 Jun 2023, 06:22 • Replies 14 • Views 8262

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Problem Solving (PS) | Re: A certain identification code consists of 6 digits, each of which is

March 11, 2024, 5:07 am

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unicornilove wrote:

Hello, I got the 36 options but actually did it as 2*36*2*36. The reason for the *2 is because positions 1,3 and 2,4 can be switched. Could anyone explain the flaw in my logic please? Thank you

36 combinations include both (1, 2) and (2, 1) pairs.

If the 1st digit is 1, the 3rd digit could be anything from 1 to 8, giving pairs such as (1, 1), (1, 2), (1, 3), ..., (1, 8)
If the 1st digit is 2, the 3rd digit could be anything from 1 to 7, giving pairs such as (2, 1), (2, 2), (2, 3), ..., (2, 7)
...
If the 1st digit is 8, the 3rd digit could only be 1, giving (8, 1) pair.

Statistics : Posted by Bunuel • on 08 Aug 2023, 08:00 • Replies 9 • Views 10299

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Problem Solving (PS) | Re: At a certain restaurant, a meal consists of one appetizer, one main

March 11, 2024, 5:27 am

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2C1 * 3C1 * 5C1
=2*3*5
=30.

ANS B

Statistics : Posted by Jsgambach • on 11 Mar 2024, 00:30 • Replies 2 • Views 142

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Problem Solving (PS) | 150 workers were engaged to finish a piece of work in a certain number

March 11, 2024, 5:36 am

≫ Next: Problem Solving (PS) | The XYZ river flows at 12 km/hr. A boy who can row at 25/18 m/s in sti

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150 workers were engaged to finish a piece of work in a certain number of days. 4 workers dropped the second day, 4 more workers dropped the third day and so on. It takes eight more days to finish the work now. The number of days in which the work was completed is:

A. 10
B. 17
C. 20
D. 25
E. 30

Statistics : Posted by playthegame • on 11 Mar 2024, 03:36 • Replies 0 • Views 98

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Problem Solving (PS) | The XYZ river flows at 12 km/hr. A boy who can row at 25/18 m/s in sti

March 11, 2024, 6:49 am

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Bunuel wrote:

The XYZ river flows at 12 km/hr. A boy who can row at 25/18 m/s in still water had to cross it in the least possible time. The distance covered by the boy is how many times the width of the river XYZ?

A. 2.1
B. 2.3
C. 2.6
D. 2.9
E.3.0

Are You Up For the Challenge: 700 LevelQuestions

Responding to a PM.

Let us convert the speeds in same units.

Now, 1 m/s is 18/5 km/h=> $ 1 m/s =\frac{\frac{1}{1000}}{\frac{1}{3600} }km/hr =\frac{3600}{1000}=\frac{18}{5}$ km/h

Thus, the speed of the boyis $\frac{25}{18} m/s =\frac{25}{18}*\frac{18}{5}=5$ km/hr

Next, let us visualize the boat's movement due to different movements.
Boys rowing speed: This will take the boy straight across the river if acting alone.
Water speed: This will take the boy down the river if acting alone.

So, we have one force taking him across and the other down, that is it makes a L shape, where vertical line of L is the width covered by boy and horizontal line in L covered by river.
When these two forces are combined, the boy will move obliquely from the open end
...

Statistics : Posted by chetan2u • on 29 Dec 2021, 06:15 • Replies 2 • Views 5624

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Problem Solving (PS) | Re: A hall has space for t tables of equal length running along its center

March 11, 2024, 7:32 am

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Statistics : Posted by bumpbot • on 27 Feb 2023, 11:00 • Replies 3 • Views 1746

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Problem Solving (PS) | Re: A new employee in a mobile store has been assigned to mark defective p

March 11, 2024, 7:43 am

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Statistics : Posted by bumpbot • on 16 Apr 2019, 08:27 • Replies 4 • Views 2392

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Problem Solving (PS) | Re: If n = (33)^43 + (43)^33 what is the units digit of n?

March 11, 2024, 7:58 am

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Gmatguy007 wrote:

Archit143 wrote:

If $n = 33^{43} + 43^{33}$ what is the units digit of n?

A. 0
B. 2
C. 4
D. 6
E. 8

PS00564

In order to be sure for the understanding of the method, if we had to find the unit digit of 47^26 + 26^47 we would focus on the 7^6 which gives us unit digit 9 and 6^7 with unit digit 9. So the unit digit of 47^26 + 26^47 is 9+6 = 15, am I correct?

__________________
Yes, you are right.

Statistics : Posted by Bunuel • on 03 Oct 2012, 23:13 • Replies 17 • Views 183118

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Problem Solving (PS) | Re: The organizers of a conference offered a certain number

March 11, 2024, 8:05 am

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KarishmaB wrote:

chetan2u wrote:

At least 93 would mean 93 ormore.

Take option D.
So you had 20 seminars initially. Total attending: 18*20 or 360

Now, due to space constraints, 16 of them accommodated 15, so 16*15 or 240 catered for in these 16rooms.
What aboutbalance ? They are left with 4 roomsonly.
How many areleft ? 360-240 or120
Is it at least93 ? Yes

D meets all criteria for being correct answer. Similarly other choices too.
Reason for all to meet the answer is only one and that is ‘at least93’.

Consider thisChetan: The organizers of a conference offered a certain number of simultaneous seminars with the intention that each seminar would be attended by 18 conferenceattendees.

So the number of attendees is fixed. n is chosen so that exactly 18 people go to each.

The only reason "at least 93" is used is to balance out "allowed only upto 15 attendees".

If fewer than 15 attendees (each) go to the (n-4) seminars, then we will end up having more than
...

Statistics : Posted by chetan2u • on 01 May 2017, 00:59 • Replies 22 • Views 10843

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Problem Solving (PS) | Re: The absolute value of (x + a) will be the greatest if x is the coordin

March 11, 2024, 8:22 am

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Problem Solving (PS) | Re: If the price of a certain computer increased 30 percent from d dollars

March 11, 2024, 8:29 am

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Bunuel wrote:

If the price of a certain computer increased 30 percent from d dollars to 351 dollars, then 2d =

A. 540
B. 570
C. 619
D. 649
E. 700

351/(100 + 30)/100 = 270 = d

Thus, 2d = 540, Answer must be (A)

Statistics : Posted by Abhishek009 • on 11 Mar 2024, 00:30 • Replies 3 • Views 170

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Problem Solving (PS) | Re: A parabola has one x-intercept at ( 4, 0). If the vertex is at (2, 5

March 11, 2024, 8:42 am

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Problem Solving (PS) | Re: The ratio of a two digit number to a number formed by reversing its di

March 11, 2024, 8:50 am

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DisciplinedPrep wrote:

The ratio of a two digit number to a number formed by reversing its digits is 4:7. Which of the following is the sum of all the numbers of all such pairs?

A. 110
B. 200
C. 330
D. 88
E.770

$\frac{ 10a + b}{10b +a} =\frac{4}{7}$

Or,$ 70a + 7b = 40b +4a$

Or,$ 66a =33b$

Or,$ 2a =b$

Now plug in possible values of a and b for a 2 digit no-

Attachment:

Screenshot 2024-03-11 200935.png

neglect a = 10 and b =5 as 2 digit no can not be formed when a = 10

Now, find 10a +b

Attachment:

10a + b.png

Again form 10b +a

Attachment:

10b + a.png

Now add (10a + b) + (10b + a):

Attachment:

10a + b + 10b +a.png

Here all the values :$ 33 + 66 + 99 + 132 =330$ , Answer must be (C)

...

Attachments

10a + b + 10b +a.png [ 4.1 KiB | Viewed 53 times ]

10b + a.png [ 1.58 KiB | Viewed 54 times ]

10a + b.png [ 1.68 KiB | Viewed 54 times ]

Screenshot 2024-03-11 200935.png [ 2.04 KiB | Viewed 56 times ]

Statistics : Posted by Abhishek009 • on 16 Jun 2019, 23:15 • Replies 4 • Views 2362

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Problem Solving (PS) | Re: Working alone, Printers X, Y, and Z can do a certain printing job, con

March 11, 2024, 8:59 am

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Statistics : Posted by bumpbot • on 05 Mar 2014, 01:16 • Replies 13 • Views 55129

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Problem Solving (PS) | Re: Kiana has two older twin brothers. The product of their three ages is

March 11, 2024, 9:13 am

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Bunuel wrote:

Kiana has two older twin brothers. The product of their three ages is 128. What is the sum of their three ages?

(A) 10
(B) 12
(C) 16
(D) 18
(E) 24

$e^2*K = 128$

Or, $e^2*K = 2^7$

Now,$2^{3*2}*2 = 2^7$

Since, $e > K$

We have $e = 8$ & $k = 2$

Sum of their ages is $8 + 8 + 2 = 18$, Answer must be (D)

Statistics : Posted by Abhishek009 • on 28 Mar 2019, 22:35 • Replies 4 • Views 3406

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