The Sum of Two Positive Integers is 156 and Their Highest Common Factor is 13 GMAT Problem Solving

Question: The sum of two positive integers is 156 and their highest common factor is 13. How many pairs of such numbers are possible?

1. 1
2. 2
3. 3
4. 4
5. 5

Correct Answer: B
Solution and Explanation:
Approach Solution 1:

First number= 13a
The second number is 13b, and is co-prime (roughly prime), hence their HCF is 1.
13a+13b = 156
i.e. a+b = 12

i.e (a,b) = (1, 11) (2, 10) (3, 9) (4, 8) (5, 7) (6, 6)
i.e. only two such pairs
Hence the correct answer is B.

Approach Solution 2:

There is just one component that unites two numbers, and that factor is 13, hence two numbers only have 13 in common.
Thus, let 13A and 13B be the two numbers.
13(A+B)=156

A+B=12
As previously stated, A and B will now be co-primes (have no common factor other than 1)
A and B might therefore have values of (1,11) and (5,7).
The maximum number of pairings is two.

Hence the correct answer is B.

Approach Solution 3:

As , 13 is the highest common factor of two number and sum of 2 is 156,
Therefore, 13x+13y = 156
13(x+y) = 156 ------ 1
x+y = 12 ( where x & y has to be co-primes)

Now we have to check values for x & y.
If x = 1, then y = 11 ; put in 1, so the sum is 156.
If x= 5 , then y = 7 ; put in 1, so the sum is 156.

So only 2 pairs are possible.
Hence the correct answer is B.

“The sum of two positive integers is 156 and their highest common factor is 13. How many pairs of such numbers are possible?” - 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 Samples

• How many Terminating Zeroes does 200! Have? GMAT Problem Solving
• 1511−151014=? GMAT Problem Solving
• If g is an integer what is the value of(−1)g4−1(−1)g4−1? GMAT Problem Solving
• What is the Area of the Triangle with the following Vertices L(1,3) M(5,1) and N(3,5)? GMAT Problem Solving
• If P2−QR=10P2−QR=10 ,Q2+PR=10Q2+PR=10 ,R2+PQ=10R2+PQ=10 GMAT Problem Solving
• If 298=256L+N298=256L+N , Where L and N are Integers and 0≤N≤40≤N≤4 , What is the Value of N? GMAT Problem Solving
• How Many 5-Letter Words can be Formed Using the Letters of the English Alphabet that Contain 2 Different Vowels GMAT Problem Solving
• If a+b+c = 0 and a^3+b^3+c^3 = 216, What is the Value of a∗b∗c ? GMAT Problem Solving
• If a Polygon has 44 Diagonals, Then How Many Sides are There in the Polygon? GMAT Problem Solving
• If (a1 + a2 + a3 + .... +an) = 3(2n+1 - 2), For Every n≥1, Then a11 Equals GMAT Problem Solving
• A Chord of a Circle is Equal to its Radius. GMAT Problem Solving
• A Clock loses a Minute Every Three Hours for 4 Days and Gains 1% in the Subsequent 6 Days. GMAT Problem Solving
• A Container in the Shape of a Right Circular Cylinder is 1/2 Full of Water. GMAT Problem Solving
• How Many Multiples of 7 are there Between 21 and 343, Exclusive? GMAT Problem Solving
• If y (u-c) = 0 and j (u-k) = 0, Which of the Following Must be True, Assuming c < kc < k? GMAT Problem Solving
• What is the Remainder when 333^222 is Divided by 7? GMAT Problem Solving
• In a College of 300 Students, Every Student Reads 5 Newspapers and every Newspaper is Read by 60 Students GMAT Problem Solving
• If 4 People are Selected from a Group of 6 Married Couples, What is the Probability That none of Them would be Married GMAT Problem Solving
• If the Equation |x|+|y|= 5 Encloses a Certain Region on the Graph, What is the Area of that Region? GMAT Problem Solving
• If x = ¾ and y = ⅖ , What is the Value of √(x2+6x+9)(x2+6x+9) - √(y2−2y+1)(y2−2y+1)? 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
• Given f(x) = x/(x + 1), For What Value k Does f(f(k)) = 2/3 ? GMAT Problem Solving
• Which of the Following Expressions CANNOT have a Negative Value? GMAT Problem Solving
• The Figure Shown Above Consists of a Shaded 9-Sided Polygon GMAT Problem Solving
• A list of measurements in increasing order is 4, 5, 6, 8, 10 and x GMAT Problem Solving
• Rahul Can Finish a Job in 30 Days GMAT Problem Solving
• The Price of Raw Materials Has Gone up by 15% GMAT Problem Solving
• In a Class of 100 Students 70 Passed in Physics, 62 Passed in Mathematics, GMAT Problem Solving
• If x and y Are Positive Odd Integers, And Both Numbers Have An Odd Number Of Positive Divisors GMAT Problem Solving
• Copper Pipe Costs x Cents Per Foot in 8-Foot Lengths GMAT Problem Solving
• Find The Smallest Positive 4-Digit Number Which, When Increased by 8, is Divisible by 12, 18, 30, and 45 GMAT Problem Solving
• How Much Pure Alcohol Should Be Added To 400 ml of a 15% Solution To Make The Strength Of The Solution 32%? GMAT Problem Solving
• If n = 3, What is The Value of 2^2n+1? GMAT Problem Solving
• The First Five Numbers in a Regular Sequence are 4, 10, 22, 46, and 94 GMAT Problem Solving
• The Volume of a Sphere With Radius r is (4/3)*pi*r^3 and the Surface Area is 4*pi*r^2 GMAT Problem Solving
• Which of the Following is Equal to 5^17×4^9? GMAT Problem Solving
• In a Shooting Competition, Probability of A Hitting Target is 2/5, by B is 2/3 and C is 3/5 GMAT Problem Solving
• The Sides of a Quadrilateral Taken in Order are 16,16,14 and 10 GMAT Problem Solving
• If 80 Lamps Can Be Lighted, 5 Hours Per Day For 10 Days GMAT Problem Solving
• If denotes the area of a circle with diameter d, then which of the following is equal to <4>*<6> GMAT Problem Solving
• If @ x=x^2/2x^2-2 , 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 circle with a radius R is inscribed into a square with a side K GMAT Problem Solving
• The square of \(5^\sqrt2)\ =? GMAT Problem Solving
• A farm has chickens, cows and sheep GMAT Problem Solving