Question: If x > 0, how many integer values of (x, y) will satisfy the equation 5x + 4|y| = 55?
A. 3
B. 6
C. 5
D. 4
E. 2
Answer:
Approach Solution (1):
t = x + y
4t + x = 55 → x = 55 - 4t
y = t - x = t - (55 - 4t) = -55 + 5t
x>0 → 55 - 4t > 0 → 55 > 4t → 13.75 > t
As long as the integer t <= 13, all points (55 - 4t, -55 + 5t) are solutions.
If there is no restriction on y, there are indefinitely many points.
t = 13: (3, 10)
t = 12: (7, 5)
t = 11: (11, 0)
t = 10: (15, -5)
t = 0: (55, -55)
Correct option: C
Approach Solution (2):
5x + 4|y| = 55
The equation can be rewritten as 4|y| = 55 - 5x.
Inference 1: Because |y| is non-negative, 4|y| will be non-negative.
Therefore, (55 - 5x) cannot take negative values.
Inference 2: Because x and y are integers, 4|y| will be a multiple of 4.
Therefore, (55 - 5x) will also be a multiple of 4.
Inference 3: 55 is a multiple of 5. 5x is a multiple of 5 for integer x.
So, 55 - 5x will always be a multiple of 5 for any integer value of x.
Combining Inference 2 and Inference 3: 55 - 5x will be a multiple of 4 and 5.
i.e., 55 - 5x will be a multiple of 20.
Integer values of x > 0 that will satisfy the condition that (55 - 5x) is a multiple of 20:
1. x = 3, 55 - 5x = 55 - 15 = 40.
2. x = 7, 55 - 5x = 55 - 35 = 20
3. x = 11, 55 - 5x = 55 - 55 = 0.
When x = 15, (55 - 5x) = (55 - 75) = -20.
Because (55 - 5x) has to non-negative, x = 15 or values greater than 15 are not possible.
So, x can take only 3 values viz., 3, 7, and 11.
Possible values of y when x = 3, x = 7, and x = 11
We have 3 possible values for 55 - 5x. So, we will have these 3 values possible for 4|y|.
Possibility 1: 4|y| = 40 or |y| = 10. So, y = 10 or -10.
Possibility 2: 4|y| = 20 or |y| = 5. So, y = 5 or -5.
Possibility 3: 4|y| = 0 or |y| = 0. So, y = 0.
Number of values possible for y = 5
Correct option: C
Approach Solution (3):
The equation will be
5x + 4y = 55, when y > or = 0
Considering integer solution, (x, y) can be (3, 10) (7, 5) (11, 0)
5x – 4y = 55, when y < 0
Considering integer solutions, (x, y) can be (3, -10) (7, -5)
Hence there will be 5 integral solutions
Correct option: C
“If x > 0, how many integer values of (x, y) will satisfy the equation 5x + 4|y| = 55?”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “GMAT Official Guide Quantitative Review”. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. The GMAT Quant topic in the problem-solving part requires calculative mathematical problems that should be solved with proper mathematical knowledge.
Suggested GMAT Problem Solving Questions:
- Find The Altitude Of An Equilateral Triangle Whose Side is 20 GMAT Problem Solving
- Which of the following is the value of √3√0.000064? GMAT Problem Solving
- Two Dice are Thrown Simultaneously. What is the Probability of Getting Two Numbers Whose Product is Even? GMAT Problem Solving
- The Smallest 3-Digit Positive Integer Obtained By Adding Two Positive Two-Digit Numbers GMAT Problem Solving
- Train A Leaves New York at 9am Eastern Time on Monday, Headed for Los Angeles at a Constant Rate GMAT Problem Solving
- An Express Train Traveled At An Average Speed of 100 Kilometers Per Hour GMAT Problem Solving
- If m Lies Between The Integers p and s On the Number Line Shown GMAT Problem Solving
- A Cube Of Side 7 cm Is Coloured On Pair of Opposite Faces By Red, Green and Yellow Shades GMAT Problem Solving
- If x2 − 5x − 6 = 0, which of the following could be x ? GMAT Problem Solving
- How Many Numbers Between 1 and 1000, Inclusive Have an Odd Number of Factors? GMAT Problem Solving
- GMAT Problem Solving- Given f(x) = x/(x + 1), For What Value k Does f(f(k)) = 2/3 ?
- Which Among the Following is the Smallest 7-digit Number that is Exactly Divisible by 43? GMAT Problem Solving
- During a Trip, Francine Traveled x Percent of the Total Distance at an Average Speed of 40 Miles GMAT Problem Solving
- Which of the Following Expressions CANNOT have a Negative Value? GMAT Problem Solving
- Which of the following is greatest? GMAT Problem Solving
- The Cost Price of 20 Articles is The Same as The Selling Price of x Articles GMAT Problem Solving
- In The Figure Shown, If The Area of The Shaded Region is 3 Times The Area of The Smaller Circular Region GMAT Problem Solving
- A Regular Hexagon has a Perimeter of 30 units GMAT Problem Solving
- All the Numbers 2, 3, 4, 5, 6, 7 are Assigned to the Six Faces of a Cube, One Number to Each Face GMAT Problem Solving
- If it is true that x > -2 and x < 7, which of the following must be true? GMAT Problem Solving
- In a Drawer, There are 4 White Socks, 3 Blue Socks, and 5 Grey Socks GMAT Problem Solving
- There are 100 Apples in a Bag of which 98% are Green and Rest are Red GMAT Problem Solving
- A palindrome is a number that reads the same forward and backwardGMAT Problem Solving
- Three Cars Leave From A To B In Equal Time Intervals GMAT Problem Solving
- An Inlet Pipe can Fill in an Empty Cistern in 30 minutes GMAT Problem Solving
- A Zookeeper Counted the Heads of the Animals in a Zoo and Found it to be 80 GMAT Problem Solving
- A Shop Stores x kg of Rice. The First Customer Buys half this Amount Plus half a kg of Rice GMAT Problem Solving
- In a Class of 120 Students Numbered 1 to 120, All Even Numbered Students Opt for Physics GMAT Problem Solving
- Machine A Produces bolts at a Uniform Rate of 120 Every 40 seconds GMAT Problem Solving
- Out of 7 Consonants and 4 Vowels, How Many Words of 3 Consonants and 2 Vowels Can be Formed? GMAT Problem Solving
- 4 Bells Toll Together at 9:00 A.M. They Toll After 7, 8, 11 and 12 Seconds GMAT Problem Solving
- 12 Marbles are Selected at Random from a Large Collection of White, Red, Green and Yellow Marbles GMAT Problem Solving
- Find the greatest number that will divide 43, 91 and 183 GMAT Problem Solving
- Of the 150 Houses in a Certain Development GMAT Problem Solving
- A man can hit a target once in 4 shots. If he fires 4 shots in succession GMAT Problem Solving
- If 75 Percent of a Class Answered the First Question on a Certain Test Correctly GMAT Problem Solving
- A Clock Strikes 4 taking 9 seconds.GMAT Problem Solving
- What is the Largest Power of 3 Contained in 200! GMAT Problem Solving
- Find The Value Of x GMAT Problem Solving
- GMAT Problem Solving – Which of the following expressions has the greatest values?
- GMAT Problem Solving – If @ x=x2/2x2-2 , What is the Units Digit of @ (@4)?
- GMAT Problem Solving – What is the product of all possible solutions of the equation |x+2|- 5|x+2| = -6?
- GMAT Problem Solving – Metropolis Corporation has 4 Shareholders
- GMAT Problem Solving – What is the number of integers from 1 to 1000, inclusive that are not divisible by 11 or by 35?
- GMAT Problem Solving – If m is Three Times n, and if 2n + 3 is 20% of 25, What is the value of m?
- GMAT Problem Solving – If Ben Were to Lose the Championship, Mike would be the Winner
- GMAT Problem Solving – A Train Travelling at a Certain Constant Speed takes 30 seconds
- GMAT Problem Solving – A conference room is equipped with a total of 45 metal or wooden chairs.
- GMAT Problem Solving – A welder received an order to make a 1 million litre cube-shaped tank.
- GMAT Problem Solving – After 6 games, Team B had an average of 61.5 points per game.