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If |x^2-x+1|=2x-1

Case 1:
=> x^2 - x + 1 = 2x - 1
x^2 - 3x + 2 = 0
(x-2)(x-1) = 0
x = 1/2

Case 2:
=> x^2 - x + 1 = -2x + 1
x^2 + x = 0
x(x+1) = 0
x = 0/-1

But for both these values RHS is < 0 but LHS is modulus which cannot be negative so we reject these 2 values

Sum = 1+2 = 3
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If |x^2-x+1|=2x-1

Case 1:
=> x^2 - x + 1 = 2x - 1
x^2 - 3x + 2 = 0
(x-2)(x-1) = 0
x = 1/2

Case 2:
=> x^2 - x + 1 = -2x + 1
x^2 + x = 0
x(x+1) = 0
x = 0/-1

But for both these values RHS is < 0 but LHS is modulus which cannot be negative so we reject these 2 values

Sum = 1+2 = 3
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gmatophobia
Another one - Problem Solving

If |x | + |y | = -x – y and xy does not equal 0, which of the following must be true?

A. x + y > 0
B. x + y 0
D. x – y 0

Source: Manhattan GMAT | Difficulty : Medium
B.

gmatophobia
Another one - Problem Solving

If |x | + |y | = -x – y and xy does not equal 0, which of the following must be true?

A. x + y > 0
B. x + y 0
D. x – y 0

Source: Manhattan GMAT | Difficulty : Medium
If both are negative
|x| = -x if x is negative else+x
|y| = -y if y is negative else +y

Which means that both numbers are negative
Then their sun will also ve less than 0
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gmatophobia
Another one - Problem Solving

If |x | + |y | = -x – y and xy does not equal 0, which of the following must be true?

A. x + y > 0
B. x + y 0
D. x – y 0

Source: Manhattan GMAT | Difficulty : Medium
B ?
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gmatophobia
Another one - Problem Solving

If |x | + |y | = -x – y and xy does not equal 0, which of the following must be true?

A. x + y > 0
B. x + y 0
D. x – y 0

Source: Manhattan GMAT | Difficulty : Medium
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Data Sufficiency

On Jane’s credit card account, the average daily balance for 30-day billing cycle is the average (arithmetic mean) of the daily balances at the end of each of the 30 days. At the beginning of a certain 30-day billing cycle, Jane’s credit card account had a balance of $600. Jane made a payment of $300 on the account during the billing cycle. If no other amounts were added to or subtracted from the account during the billing cycle, what was the average daily balance on Jane’s account for the billing cycle?

(1) Jane’s payment was credited on the 21st day of the billing cycle.

(2) The average daily balance through the 25th day of the billing cycle was $540.

Source: Official Guide | Difficulty: Medium
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gmatophobia
Data Sufficiency

On Jane’s credit card account, the average daily balance for 30-day billing cycle is the average (arithmetic mean) of the daily balances at the end of each of the 30 days. At the beginning of a certain 30-day billing cycle, Jane’s credit card account had a balance of $600. Jane made a payment of $300 on the account during the billing cycle. If no other amounts were added to or subtracted from the account during the billing cycle, what was the average daily balance on Jane’s account for the billing cycle?

(1) Jane’s payment was credited on the 21st day of the billing cycle.

(2) The average daily balance through the 25th day of the billing cycle was $540.

Source: Official Guide | Difficulty: Medium

Nov 07 - Question of the day

The median of n consecutive odd integers is 30. If the fifth term is 33, then which of the following can be the last term of the sequence?

A.19
B.21
C.25
D.33
E.41

Source: eGMAT | Difficulty : Hard
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E.41
Nice try ! :)

Infact when I solve this first, I was also about to select 41. However I realized something was off when I rechecked the question.

Hint: 33 is the 5th term.
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gmatophobia
Nov 07 - Question of the day

The median of n consecutive odd integers is 30. If the fifth term is 33, then which of the following can be the last term of the sequence?

A.19
B.21
C.25
D.33
E.41

Source: eGMAT | Difficulty : Hard

Nov 07 - DS Question of the day

If x and y are positive integers, what is the value of x?

1) When 9x is divided by 2y, the quotient is x, and the remainder is 5
2) When 5y is divided by x, the quotient is y, and the remainder is 0

Source: GMATPrepNow | Difficulty : Hard
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gmatophobia
Nov 07 - DS Question of the day

If x and y are positive integers, what is the value of x?

1) When 9x is divided by 2y, the quotient is x, and the remainder is 5
2) When 5y is divided by x, the quotient is y, and the remainder is 0

Source: GMATPrepNow | Difficulty : Hard
D ?
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gmatophobia
Nov 07 - DS Question of the day

If x and y are positive integers, what is the value of x?

1) When 9x is divided by 2y, the quotient is x, and the remainder is 5
2) When 5y is divided by x, the quotient is y, and the remainder is 0

Source: GMATPrepNow | Difficulty : Hard
B?
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Guys if possible, please share the working as well. It will help everyone.

HSogani
gmatophobia
Nov 07 - DS Question of the day

If x and y are positive integers, what is the value of x?

1) When 9x is divided by 2y, the quotient is x, and the remainder is 5
2) When 5y is divided by x, the quotient is y, and the remainder is 0

Source: GMATPrepNow | Difficulty : Hard
B?
Well tried !

I guess you rejected A because you’re getting two possible values of x and y, is that correct ?

I will give you a hint : Remainder is non negative, and is always less than the divisor. I believe you may want to check once in the light of this reasoning.
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HSogani
gmatophobia
Nov 07 - DS Question of the day

If x and y are positive integers, what is the value of x?

1) When 9x is divided by 2y, the quotient is x, and the remainder is 5
2) When 5y is divided by x, the quotient is y, and the remainder is 0

Source: GMATPrepNow | Difficulty : Hard
B?
Well tried !

I guess you rejected A because you’re getting two possible values of x and y, is that correct ?

I will give you a hint : Remainder is non negative, and is always less than the divisor. I believe you may want to check once in the light of this reasoning.
A, bcoz with B we are getting y=0 which means that x can have any value
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The stem says that x and y are positive integers, so it cannot be zero :)
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The stem says that x and y are positive integers, so it cannot be zero :)
yes, forgot that. It must be D then
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Awesome everyone. This is indeed a difficult tricky question.
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gmatophobia
Nov 07 - DS Question of the day

If x and y are positive integers, what is the value of x?

1) When 9x is divided by 2y, the quotient is x, and the remainder is 5
2) When 5y is divided by x, the quotient is y, and the remainder is 0

Source: GMATPrepNow | Difficulty : Hard

Happy Monday Everyone ! (Friday is just 4 days away :lol: )

Please feel free to post questions , strategies and anything that you feel relevant to GMAT.

Let’s crack this together. :thumbsup: :thumbsup:
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