4^8 + 4^8 + 4^8 + 4^8 = 4 X 4^8 = 4^(8+1) = 4^9

Thus, x = 9.

]]>

4^8 + 4^8 + 4^8 + 4^8 = 4 X 4^8 = 4^(8+1) = 4^9

Thus, x = 9.]]>

{x, y, z}

If the first term in the data set above is 3, what is the third term?

(1) The range of this data set is 0.

(2) The standard deviation of this data set is 0

A set, by definition, is a collection of elements without any order. (While, a sequence, by definition, is an ordered list of terms.)So, it makes no sense talking about first term in the set.

]]>

{x, y, z}

If the first term in the data set above is 3, what is the third term?

(1) The range of this data set is 0.

(2) The standard deviation of this data set is 0

A set, by definition, is a collection of elements without any order. (While, a sequence, by definition, is an ordered list of terms.)So, it makes no sense talking about first term in the set.]]>

I get putting in f(x) for x in to the equation for f(y). This results in:

f(y) = [((x + 1) / (x-1)) + 1] / [((x+1) / (x-1))-1]

can someone illustrate the simplification steps to get to f(y) = x ? It's not apparent to me from these explanations.

Hijjamieson42

Let me try to explain.

Given\(f(x) = \frac{x+1}{x-1}, x \neq 1\) and\(y = f(x)\)

\(f(y) =\frac{ \frac{x+1}{x-1} + 1}{\frac{x+1}{x-1} - 1} = \frac{\frac{x + 1 + x - 1}{x-1}}{\frac{x+1 - x + 1}{x-1}} = \frac{2x}{2} = x\)

Hope it helps.

We can solve this question

...

]]>

I get putting in f(x) for x in to the equation for f(y). This results in:

f(y) = [((x + 1) / (x-1)) + 1] / [((x+1) / (x-1))-1]

can someone illustrate the simplification steps to get to f(y) = x ? It's not apparent to me from these explanations.

Hijjamieson42

Let me try to explain.

Given\(f(x) = \frac{x+1}{x-1}, x \neq 1\) and\(y = f(x)\)

\(f(y) =\frac{ \frac{x+1}{x-1} + 1}{\frac{x+1}{x-1} - 1} = \frac{\frac{x + 1 + x - 1}{x-1}}{\frac{x+1 - x + 1}{x-1}} = \frac{2x}{2} = x\)

Hope it helps.

We can solve this question

...]]>

Hi Bunuel,

I don't know if this approach is right. I got the answer though

distance = speed x time

60 = (30 + 60) x time

60 = 90 x time

60/90 = time

2/3 multiplied by 60 = 40

Therefore, the answer is B. Is my approach correct?

No, that;'s not correct.

Distance = Average Speed * Time.

Distance = 60;

Time = 30/30 + 30/60 = 3/2 hours;

60 = Average Speed * 3/2

Average Speed = 40.

...

]]>

Hi Bunuel,

I don't know if this approach is right. I got the answer though

distance = speed x time

60 = (30 + 60) x time

60 = 90 x time

60/90 = time

2/3 multiplied by 60 = 40

Therefore, the answer is B. Is my approach correct?

No, that;'s not correct.

Distance = Average Speed * Time.

Distance = 60;

Time = 30/30 + 30/60 = 3/2 hours;

60 = Average Speed * 3/2

Average Speed = 40.

...]]>

Answer is E.

BTW, can OA be wrong?

Edited the OA. It's E, not A.

]]>

Answer is E.

BTW, can OA be wrong?

Edited the OA. It's E, not A.]]>

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]]>

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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If x is equal to 1 more than the product of 3 and z, and y is equal to 1 lessthan the product of 2 and z, then 2x is how much greater than 3y when z is 4?

(A) 1

(B) 2

(C) 3

(D) 5

(E) 6

]]>

If x is equal to 1 more than the product of 3 and z, and y is equal to 1 lessthan the product of 2 and z, then 2x is how much greater than 3y when z is 4?

(A) 1

(B) 2

(C) 3

(D) 5

(E) 6]]>

1. a > b

There are multiple possibilities for a & b and is thus insufficient.

2. a and b share only one factor

Let a=15 & b=10. They share one factor 5. But this does not give us a/b as an integer(1.5).

Thus this is also not sufficient.

Combining statement 1 & 2, with the above example, we can conclude that this is also not sufficient.

Thus, the answer is E.

]]>

1. a > b

There are multiple possibilities for a & b and is thus insufficient.

2. a and b share only one factor

Let a=15 & b=10. They share one factor 5. But this does not give us a/b as an integer(1.5).

Thus this is also not sufficient.

Combining statement 1 & 2, with the above example, we can conclude that this is also not sufficient.

Thus, the answer is E.]]>

(1) The dealership sold three times as many blue coupes as red sedans last year.

(2) The dealership sold half as many blue sedans as blue coupes last year.

]]>

(1) The dealership sold three times as many blue coupes as red sedans last year.

(2) The dealership sold half as many blue sedans as blue coupes last year.]]>

Chris’s convertible gets gas mileage that is 40 percent higher than that of Stan’s SUV. If Harry’s hatchback gets gas mileage that is 15 percent higher than that of Chris’s convertible, then Harry’s hatchback gets gas mileage that is what percent greater than that of Stan’s SUV?

(A) 25%

(B) 46%

(C) 55%

(D) 61%

(E) 66%

Hi,

Stan's SUV : X

Chris Convertible : 1.4X

Harry's Hatchback : 1.15* (1.4X)

Stan's SUV to Harry's hatchback is X to 1.15*(1.4X) or X to 1.61X

Harry’s hatchback

...

]]>

Chris’s convertible gets gas mileage that is 40 percent higher than that of Stan’s SUV. If Harry’s hatchback gets gas mileage that is 15 percent higher than that of Chris’s convertible, then Harry’s hatchback gets gas mileage that is what percent greater than that of Stan’s SUV?

(A) 25%

(B) 46%

(C) 55%

(D) 61%

(E) 66%

Hi,

Stan's SUV : X

Chris Convertible : 1.4X

Harry's Hatchback : 1.15* (1.4X)

Stan's SUV to Harry's hatchback is X to 1.15*(1.4X) or X to 1.61X

Harry’s hatchback

...]]>

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]]>

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A comedian is playing two shows at a certain comedy club, and twice as many tickets have been issued for the evening show as for the afternoon show. Of the total number of tickets issued for both shows, what percentage has been sold?

(1) A total of 450 tickets have been issued for both shows.

(2) Exactly 3/5 of the tickets issued for the afternoon show have been sold, and 1/5 exactly of the tickets issued for the evening show have been sold

Hi,

It is very nice question and thanks for sharing

...

]]>

A comedian is playing two shows at a certain comedy club, and twice as many tickets have been issued for the evening show as for the afternoon show. Of the total number of tickets issued for both shows, what percentage has been sold?

(1) A total of 450 tickets have been issued for both shows.

(2) Exactly 3/5 of the tickets issued for the afternoon show have been sold, and 1/5 exactly of the tickets issued for the evening show have been sold

Hi,

It is very nice question and thanks for sharing

...]]>

(2) x – 2y < –7

]]>

(2) x – 2y < –7]]>

(1) The average (arithmetic mean) of x and y is 308.

(2) The mode of set S is 0.

]]>

(1) The average (arithmetic mean) of x and y is 308.

(2) The mode of set S is 0.]]>

]]>

NandishSS wrote:

MathRevolution wrote:

Is a=b?

1) \(a^2=b^2\)

2) \(a=2\)

1) \(a^2=b^2\)

2) \(a=2\)

HiBunuel

Can throw some light on this question

Seems like ans is E. Can you validate.

You're right; the correct answer isE

Statements 1 and 2 combined

Case a: a = 2 and b = 2, in which casea EQUALS b

Case b: a = 2 and b = -2, in which casea DOES NOT EQUAL b

Since we cannot answer thetarget question with certainty, the combined statements are NOT SUFFICIENT

Cheers,

Brent

...

]]>

NandishSS wrote:

MathRevolution wrote:

Is a=b?

1) \(a^2=b^2\)

2) \(a=2\)

1) \(a^2=b^2\)

2) \(a=2\)

HiBunuel

Can throw some light on this question

Seems like ans is E. Can you validate.

You're right; the correct answer isE

Statements 1 and 2 combined

Case a: a = 2 and b = 2, in which casea EQUALS b

Case b: a = 2 and b = -2, in which casea DOES NOT EQUAL b

Since we cannot answer thetarget question with certainty, the combined statements are NOT SUFFICIENT

Cheers,

Brent

...]]>

The conclusion of the argument, however, was about the number of generic companies that copied patented molecules illegally; this number would remain unaffected.

The argument concludes that the prosecution of a small number of companies that copy the patented molecules illegally will have a minimal impact on the overall number of companies that engage in illegal copying

If we go

...

]]>

The conclusion of the argument, however, was about the number of generic companies that copied patented molecules illegally; this number would remain unaffected.

The argument concludes that the prosecution of a small number of companies that copy the patented molecules illegally will have a minimal impact on the overall number of companies that engage in illegal copying

If we go

...]]>

○A○ 15

○B○ 18

○C○ 20

○D○ 25

○E○ 26

let w=liters of water to be added

.9*10+w=.96(10+w)

w=15

A

]]>

○A○ 15

○B○ 18

○C○ 20

○D○ 25

○E○ 26

let w=liters of water to be added

.9*10+w=.96(10+w)

w=15

A]]>

A foot race will be held on Saturday. How many different arrangements of medal winners are possible?

(1) Medals will be given for 1st, 2nd, and 3rd place.

(2) There are 10 runners in the race.

DearSajjadAhmad ,

I'm happy to help.

I assume the medals for the three places are different medals, not all the same medal. This question could have been more careful about specifying the precise details.

Here's the analysis.

...

]]>

A foot race will be held on Saturday. How many different arrangements of medal winners are possible?

(1) Medals will be given for 1st, 2nd, and 3rd place.

(2) There are 10 runners in the race.

DearSajjadAhmad ,

I'm happy to help.

I assume the medals for the three places are different medals, not all the same medal. This question could have been more careful about specifying the precise details.

Here's the analysis.

...]]>

Mike, a DJ at a high school radio station, needs to play two or three more songs before the end of the school dance. If each composition must be selected from a list of the 10 most popular songs of the year, how many unique song schedules are available for the remainder of the dance, if the songs cannot be repeated?

(A) 6

(B) 90

(C) 120

(D) 720

(E) 810

Dearvikasp99 ,

I'm happy to respond. This is another good Veritas question.

...

]]>

Mike, a DJ at a high school radio station, needs to play two or three more songs before the end of the school dance. If each composition must be selected from a list of the 10 most popular songs of the year, how many unique song schedules are available for the remainder of the dance, if the songs cannot be repeated?

(A) 6

(B) 90

(C) 120

(D) 720

(E) 810

Dearvikasp99 ,

I'm happy to respond. This is another good Veritas question.

...]]>

At a high school track tryout, there are eight women and five men competing for the three male and three female spots on the decathlon team. How many different combinations of decathletes are possible on the final team for the six spots?

(A) 112,896

(B) 3,136

(C) 560

(D) 66

(E) 18

Dearvikasp99 ,

I'm happy to respond. Like most Veritas questions, this is a great question. For computing combinations, see these two posts:

...

]]>

At a high school track tryout, there are eight women and five men competing for the three male and three female spots on the decathlon team. How many different combinations of decathletes are possible on the final team for the six spots?

(A) 112,896

(B) 3,136

(C) 560

(D) 66

(E) 18

Dearvikasp99 ,

I'm happy to respond. Like most Veritas questions, this is a great question. For computing combinations, see these two posts:

...]]>

30%~35% of the employees in a certain company have cell phones. Do at least half of the employees in the company with cell phones own their houses ?

1) 70%~75% of the employees in the Company own their houses

2) 40%~45% of the employees in the Company with their houses have cell phones

DearAustinKL ,

I'm happy to respond.

There are a few problems with this question. First of all, having a tilde symbol, ~, between two percents is mathematically meaningless. I don't know whether this is how

...

]]>

30%~35% of the employees in a certain company have cell phones. Do at least half of the employees in the company with cell phones own their houses ?

1) 70%~75% of the employees in the Company own their houses

2) 40%~45% of the employees in the Company with their houses have cell phones

DearAustinKL ,

I'm happy to respond.

There are a few problems with this question. First of all, having a tilde symbol, ~, between two percents is mathematically meaningless. I don't know whether this is how

...]]>

If you are buying a product by rounding up to a $1 digit, is the sum of the differences between buying a product as its actual price and buying a product by rounding up to a $1 digit less than $12?

1) The sum of the differences in the total of 80% of the products bought is less than $10.

2) A total of 20 products were bought

DearAustinKL ,

I'm happy to respond.

My friend, the wording on this problem is truly atrocious.

...

]]>

If you are buying a product by rounding up to a $1 digit, is the sum of the differences between buying a product as its actual price and buying a product by rounding up to a $1 digit less than $12?

1) The sum of the differences in the total of 80% of the products bought is less than $10.

2) A total of 20 products were bought

DearAustinKL ,

I'm happy to respond.

My friend, the wording on this problem is truly atrocious.

...]]>

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(1)

Let's say the set is (10, 20, 30). The mean is 20. The median is also 20.

Next, try (19, 20, 21). The mean is 20. The median is also 20.

It seems like whenever we have one element larger than 20,

...

]]>

(1)

Let's say the set is (10, 20, 30). The mean is 20. The median is also 20.

Next, try (19, 20, 21). The mean is 20. The median is also 20.

It seems like whenever we have one element larger than 20,

...]]>

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'What percent' = p/100

'of 112' = multiply by 112

'is' = equals sign

'14' = the number 14

So, the equation to solve is (x/100)(112) = 14. Approximate from here: 14*100/112 should be just a bit smaller than 14, so 12.5 is the only reasonable answer.

]]>

'What percent' = p/100

'of 112' = multiply by 112

'is' = equals sign

'14' = the number 14

So, the equation to solve is (x/100)(112) = 14. Approximate from here: 14*100/112 should be just a bit smaller than 14, so 12.5 is the only reasonable answer.]]>

]]>

A furniture dealer purchased a desk for $150 and then set the selling price equal to the purchase price plus a markup that was 40% of the selling price. If the dealer sold the desk at the selling price, what was the amount of the dealer's gross profit from the purchase and the sale of the desk?

A. $40

B. $60

C. $80

D. $90

E. $100

my solution:

\(150(1+\frac{x}{100})=S\) S is selling price. X is the markup.

also\(x=\frac{4}{10}S\)

substitute:\(150(1+\frac{4s}{10/100})=S\)

\(150+\frac{6s}{10}=S\)

\(1500+6S=10S\)

Selling

...

]]>

A furniture dealer purchased a desk for $150 and then set the selling price equal to the purchase price plus a markup that was 40% of the selling price. If the dealer sold the desk at the selling price, what was the amount of the dealer's gross profit from the purchase and the sale of the desk?

A. $40

B. $60

C. $80

D. $90

E. $100

my solution:

\(150(1+\frac{x}{100})=S\) S is selling price. X is the markup.

also\(x=\frac{4}{10}S\)

substitute:\(150(1+\frac{4s}{10/100})=S\)

\(150+\frac{6s}{10}=S\)

\(1500+6S=10S\)

Selling

...]]>

Tough and Tricky questions: Percents.

The number of students enrolled at school\(X\) this year is 7 percent more than it was last year. The number of students enrolled at school\(Y\) this year is 3 percent more than it was last year. If school\(X\) grew by 40 more students than school\(Y\) did, and if there were 4000 total enrolled students last year at both schools, how many students were enrolled at school\(Y\) last year?

A. 480

B. 1600

C. 1920

D. 2080

E.2400

Kudos for a correct solution.

...

]]>

Tough and Tricky questions: Percents.

The number of students enrolled at school\(X\) this year is 7 percent more than it was last year. The number of students enrolled at school\(Y\) this year is 3 percent more than it was last year. If school\(X\) grew by 40 more students than school\(Y\) did, and if there were 4000 total enrolled students last year at both schools, how many students were enrolled at school\(Y\) last year?

A. 480

B. 1600

C. 1920

D. 2080

E.2400

Kudos for a correct solution.

...]]>

I dont understand how you explain this without having statement numbers 1) and 2)..

Please be kind enough to explain me the explicit way to solve this.

I need your help also

mikemcgarry

Dearnishanfaith ,

I'm happy to respond. First of all, my friend, I would urge you to read through my algebraic solution step-by-step, because if you understand that, then you really will understand this problem deeply. If you understand

...

]]>

I dont understand how you explain this without having statement numbers 1) and 2)..

Please be kind enough to explain me the explicit way to solve this.

I need your help also

mikemcgarry

Dearnishanfaith ,

I'm happy to respond. First of all, my friend, I would urge you to read through my algebraic solution step-by-step, because if you understand that, then you really will understand this problem deeply. If you understand

...]]>

From what I knew, a number divided by a divisor, may/may not yield a remainder. Doesn't say anything about the divisor being a factor.

Turns out a divisor and factor are the same

]]>

From what I knew, a number divided by a divisor, may/may not yield a remainder. Doesn't say anything about the divisor being a factor.

Turns out a divisor and factor are the same ]]>

When positive integer n is divided by 3, the remainder is 2. When n is divided by 7, the remainder is 5. How many values less than 100 can n take?

(A) 0

(B) 2

(C) 3

(D) 4

(E) 5

Kudos for a correct solution.

lowest possible value of n=5

interval between successive values of n=product of divisors 3*7=21

let x=additional possible values of n

5+21x<100

x<4.5

1+4=5 possible values of n<100

E

...

]]>

When positive integer n is divided by 3, the remainder is 2. When n is divided by 7, the remainder is 5. How many values less than 100 can n take?

(A) 0

(B) 2

(C) 3

(D) 4

(E) 5

Kudos for a correct solution.

lowest possible value of n=5

interval between successive values of n=product of divisors 3*7=21

let x=additional possible values of n

5+21x<100

x<4.5

1+4=5 possible values of n<100

E

...]]>

Please tell me if my approach is right:

WRONG

(1) try different values for x that fulfill the first condition.

x = 2: (2+1)^2 = 9

x = 12: (12+1)^2 = 169

now 2^2 = 4 & 12^2 = 144 -> both have the same units digit. assuming that this will be the same also for greater numbers. (1) is sufficient

(2) again try different values that fulfill the condition

x=6: (6-1)^2 = 25

x=16: (16-1)^2 = 225

now 6^2 = 36 & 16^2 also has a units digit of 6 cause of the characteristics of 6. (2) sufficient

Answer

...

]]>

Please tell me if my approach is right:

WRONG

(1) try different values for x that fulfill the first condition.

x = 2: (2+1)^2 = 9

x = 12: (12+1)^2 = 169

now 2^2 = 4 & 12^2 = 144 -> both have the same units digit. assuming that this will be the same also for greater numbers. (1) is sufficient

(2) again try different values that fulfill the condition

x=6: (6-1)^2 = 25

x=16: (16-1)^2 = 225

now 6^2 = 36 & 16^2 also has a units digit of 6 cause of the characteristics of 6. (2) sufficient

Answer

...]]>

kamandr wrote:

I think this is a poor-quality question and the explanation isn't clear enough, please elaborate.

atreyu79 wrote:

Hi Souvik

Thank you for the reply. Based on your explanation the correct choice is:

In no other industry would firms resort to such an idiosyncratic idea such as that it is good to milk their best suppliers dry as in retail-food sector of the west.

This choice repeats such as twice and it is not clear to me.

Thanks

kamandr Let me try to explain.

First consider the following sentence:

In

...

]]>

kamandr wrote:

I think this is a poor-quality question and the explanation isn't clear enough, please elaborate.

atreyu79 wrote:

Hi Souvik

Thank you for the reply. Based on your explanation the correct choice is:

In no other industry would firms resort to such an idiosyncratic idea such as that it is good to milk their best suppliers dry as in retail-food sector of the west.

This choice repeats such as twice and it is not clear to me.

Thanks

kamandr Let me try to explain.

First consider the following sentence:

In

...]]>

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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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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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]]>

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From the answer choices, we know that there cannot be that many ways to get a total of $10.00 when adding a multiple of $0.19 and a multiple of $0.25....

A multiple of $0.25 will always end in one of the following.... .00, .25, .50 or .75... so we really just need to determine in how many ways the $0.19 ends in a 'compliment' (re: .75, .50, .25 or .00) to that number so that the total = $10.00.

To end in a 0 or a 5, we need to multiply $0.19 by a multiple of 5)....

($0.19)(0)

...

]]>

From the answer choices, we know that there cannot be that many ways to get a total of $10.00 when adding a multiple of $0.19 and a multiple of $0.25....

A multiple of $0.25 will always end in one of the following.... .00, .25, .50 or .75... so we really just need to determine in how many ways the $0.19 ends in a 'compliment' (re: .75, .50, .25 or .00) to that number so that the total = $10.00.

To end in a 0 or a 5, we need to multiply $0.19 by a multiple of 5)....

($0.19)(0)

...]]>

A and B are the end points of the longest line that can be drawn in a circle with center X. If C is a point on the circle such that AC = AX = 3, what is the perimeter of triangle ABC?

(A) 9/2

(B) 9

(C) 6 + 3 \(\sqrt{3}\)

(D) 9 + 3 \(\sqrt{3}\)

(E) 9 \(\sqrt{3}\)

DearSajjadAhmad ,

I'm happy to respond.

First, "the longest line that can be drawn in a circle quot; = the diameter. We know AB is a diameter.

X is the center, so AX & BC are radii.

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Attachments

circle X with triangle ABC.png [ 77.94 KiB | Viewed 59 times ]

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A and B are the end points of the longest line that can be drawn in a circle with center X. If C is a point on the circle such that AC = AX = 3, what is the perimeter of triangle ABC?

(A) 9/2

(B) 9

(C) 6 + 3 \(\sqrt{3}\)

(D) 9 + 3 \(\sqrt{3}\)

(E) 9 \(\sqrt{3}\)

DearSajjadAhmad ,

I'm happy to respond.

First, "the longest line that can be drawn in a circle quot; = the diameter. We know AB is a diameter.

X is the center, so AX & BC are radii.

...

Attachments

circle X with triangle ABC.png [ 77.94 KiB | Viewed 59 times ]

]]>

This question is essentially just about doing the necessary arithmetic, but if you were low on time then you can use a logic 'pattern' to quickly eliminate a bunch of answers and take a good educated guess.

Since the bottler has to 'test' 5% of the spring water and 10% of the sparkling water that it sends out, IF there were equal numbers of spring water and sparkling water, then the bottler would need to test (5% + 10%)/2 = 7.5% of the bottles. However, the prompt tells us that there

...

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This question is essentially just about doing the necessary arithmetic, but if you were low on time then you can use a logic 'pattern' to quickly eliminate a bunch of answers and take a good educated guess.

Since the bottler has to 'test' 5% of the spring water and 10% of the sparkling water that it sends out, IF there were equal numbers of spring water and sparkling water, then the bottler would need to test (5% + 10%)/2 = 7.5% of the bottles. However, the prompt tells us that there

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If I divide pie in 7 parts and take 4 I will get less then if I divide pie in 13 parts and take 7. So I picked D.

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If I divide pie in 7 parts and take 4 I will get less then if I divide pie in 13 parts and take 7. So I picked D.]]>

If q is one root of the equation x^2 + 18x + 11c = 0, where –11 is the other root and c is a constant, then q^2-c^2 =

A) 98

B) 72

C) 49

D) 0

E) It can't be determined from the information given

Product of roots=c/a

=> \(q*-11=\frac{11c}{1}\)

=>\(c=-q\)

\(q^2-c^2=q^2-(-q)^2=q^2-q^2=0\)

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If q is one root of the equation x^2 + 18x + 11c = 0, where –11 is the other root and c is a constant, then q^2-c^2 =

A) 98

B) 72

C) 49

D) 0

E) It can't be determined from the information given

Product of roots=c/a

=> \(q*-11=\frac{11c}{1}\)

=>\(c=-q\)

\(q^2-c^2=q^2-(-q)^2=q^2-q^2=0\)]]>

Rhonda runs at an average speed of 12 kilometers per hour, and she bicycles at an average speed of 30 kilometers per hour. When she bicycles to work, her travel time is 2.25 minutes less than when she runs to work. The distance to work, in kilometers, is

A) 27/40

B) 3/4

C) 7/8

D) 11/12

E) 6/5

*kudos for all correct solutions

let t=running time

12/30=(t-3/80)/t

t=1/16 hr

1/16 hr*12 kph=3/4 k distance

B

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Rhonda runs at an average speed of 12 kilometers per hour, and she bicycles at an average speed of 30 kilometers per hour. When she bicycles to work, her travel time is 2.25 minutes less than when she runs to work. The distance to work, in kilometers, is

A) 27/40

B) 3/4

C) 7/8

D) 11/12

E) 6/5

*kudos for all correct solutions

let t=running time

12/30=(t-3/80)/t

t=1/16 hr

1/16 hr*12 kph=3/4 k distance

B]]>

\((x+y)^2-(x-y)^2=?\)

1) xy=5

2) x+y=6

\((x+y)^2-(x-y)^2==>4xy=?\)

1)x+y=5 hence 4xy==>20 -- Suff

2) x+y=6--Insuff as we don't know the value of x-y.

Hence A

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\((x+y)^2-(x-y)^2=?\)

1) xy=5

2) x+y=6

\((x+y)^2-(x-y)^2==>4xy=?\)

1)x+y=5 hence 4xy==>20 -- Suff

2) x+y=6--Insuff as we don't know the value of x-y.

Hence A]]>

Together in 48 minutes, then second one fills in 80 minutes. ( 1/120 + 1/second one= 1/48 )

Let first fills x cubic meter per second then second fills (x+50) cubic meter per second

Tank capacity for first = Tank capacity for second

120 * x = 80 * (x + 50)

Solve x =100, i.e first fills at 100 and second at 150 cubic meter per minute

So tank capacity = 120 * 100 or 80*150 = 12,000

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Together in 48 minutes, then second one fills in 80 minutes. ( 1/120 + 1/second one= 1/48 )

Let first fills x cubic meter per second then second fills (x+50) cubic meter per second

Tank capacity for first = Tank capacity for second

120 * x = 80 * (x + 50)

Solve x =100, i.e first fills at 100 and second at 150 cubic meter per minute

So tank capacity = 120 * 100 or 80*150 = 12,000]]>

(A)5!/4!

(B)5!/(4!)^5

(C)20!/(5!)^4

(D)20!/(4!)^5

(E)20!/5(4!)

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(A)5!/4!

(B)5!/(4!)^5

(C)20!/(5!)^4

(D)20!/(4!)^5

(E)20!/5(4!)]]>

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Not suppose after x days 5 workers left the job. i.e 20 workers worked for x days and 15 workers worked for (35 -x) days to finish the job.

600 = 20*x + 15*(35-x)

x = 15

Ans 15 days i.e option D

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Not suppose after x days 5 workers left the job. i.e 20 workers worked for x days and 15 workers worked for (35 -x) days to finish the job.

600 = 20*x + 15*(35-x)

x = 15

Ans 15 days i.e option D]]>

What is the value of \(32xy^2+16x^2y\)?

(1) \((x+2y)^2=64\)

(2) x=2y

Greatquestion!

Target question: What is the value of 32xy² + 16x²y?

After scanning the two statements, I see that we might benefit fromrephrasing the target question .

32xy² + 16x²y = 16xy(2y + x) So.....

REPHRASED target question: What is the value of 16xy(2y + x)?

Statement 1: (x+2y)² = 64 This tells us 2 things: EITHER x+2y = 8 OR x+2y = -8

There are several values of x and y that satisfy statement 1. Here are

...

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What is the value of \(32xy^2+16x^2y\)?

(1) \((x+2y)^2=64\)

(2) x=2y

Greatquestion!

Target question: What is the value of 32xy² + 16x²y?

After scanning the two statements, I see that we might benefit fromrephrasing the target question .

32xy² + 16x²y = 16xy(2y + x) So.....

REPHRASED target question: What is the value of 16xy(2y + x)?

Statement 1: (x+2y)² = 64 This tells us 2 things: EITHER x+2y = 8 OR x+2y = -8

There are several values of x and y that satisfy statement 1. Here are

...]]>

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