Question:
The sum of two numbers is 528 and their HCF is 33. The number of pairs of such numbers that can be formed is
The sum of two numbers is 528 and their HCF is 33. The number of pairs of such numbers that can be formed is
Show Hint
For HCF problems, divide the numbers by the HCF first. Then count coprime pairs satisfying the reduced sum.
Updated On: Jul 15, 2026
- \(8\)
- \(6\)
- \(5\)
- \(4\)
Show Solution
Verified By Collegedunia
The Correct Option is D
Solution and Explanation
Concept:
If HCF of two numbers is \(33\), let the numbers be:
\[
33x \text{ and } 33y
\]
where:
\[
HCF(x,y)=1
\]
Step 1: Use the sum condition.
Given: \[ 33x+33y=528 \] \[ 33(x+y)=528 \] \[ x+y=16 \]
Step 2: Find coprime pairs whose sum is 16.
Possible pairs: \[ (1,15) \] \[ (3,13) \] \[ (5,11) \] \[ (7,9) \] Check HCF: \[ HCF(1,15)=1 \] \[ HCF(3,13)=1 \] \[ HCF(5,11)=1 \] \[ HCF(7,9)=1 \] All valid.
Step 3: Count the pairs.
Total pairs: \[ 4 \] Thus, the required answer is: \[ \boxed{4} \]
Step 1: Use the sum condition.
Given: \[ 33x+33y=528 \] \[ 33(x+y)=528 \] \[ x+y=16 \]
Step 2: Find coprime pairs whose sum is 16.
Possible pairs: \[ (1,15) \] \[ (3,13) \] \[ (5,11) \] \[ (7,9) \] Check HCF: \[ HCF(1,15)=1 \] \[ HCF(3,13)=1 \] \[ HCF(5,11)=1 \] \[ HCF(7,9)=1 \] All valid.
Step 3: Count the pairs.
Total pairs: \[ 4 \] Thus, the required answer is: \[ \boxed{4} \]
Was this answer helpful?
0
0
Top TG ICET Mathematical Ability Questions
- \[ \frac{\left(a^{\frac12}b^{-\frac16}\right)^3- \left(a^{\frac16}b^{\frac13}\right)^3} {a^{\frac12}-b^{\frac12}} = ? \]
- \[ 64^{\frac13} - 81^{\frac14} + 625^{\frac14} = ? \]
- If \(x:y=4:5\), then \((5x+4y):(10x-2y)=\ ?\)
- The ratio of milk and water in a can of 36 liters is \(3:1\). If 6 more liters of water is added, then the ratio of the milk and water will be:
- If \[ \sqrt{12+4\sqrt5} + \sqrt{16-4\sqrt7} = \sqrt{x}+\sqrt{y}, \] then find the value of \[ \sqrt{35xy}. \]
View More Questions
Top TG ICET Basic Arithmetic Questions
- If \(x:y=4:5\), then \((5x+4y):(10x-2y)=\ ?\)
- The ratio of milk and water in a can of 36 liters is \(3:1\). If 6 more liters of water is added, then the ratio of the milk and water will be:
- If the number \(7x342y\) is divisible by \(88\), then \((x,y)=\ ?\)
- The number of divisors of \(44100\) which are perfect squares is:
- If \(N\) is the largest integer that will divide \(1305\), \(4665\), and \(6905\) leaving the same remainder, then the sum of all prime numbers that divide \(N\) is:
View More Questions
Top TG ICET Questions
- What is the average of the integers 1, 2, 3, 4, and \(x\)? Statement (I): \(x\) is an even integer. Statement (II): \(x<10\)
- What is the average of \(x,y,z\) and \(t\)? Statement (I): \(x+z=12\) Statement (II): \(y+t=24\)
- What is the sum of the first 30 terms of an Arithmetic Progression? Statement (I): The common difference of the A.P. is 5. Statement (II): The first and the last terms are 2 and 60 respectively.
- In triangle \(ABC\), is \(\angle A\) obtuse? Statement (I): \(\angle C\) is acute. Statement (II): \(\angle B\) is obtuse.
- What is the circumference of the regular hexagon? Statement (I): The radius of the circumcircle of the hexagon is \(6\) cm. Statement (II): Each side of the hexagon subtends an angle of \(60^\circ\) at the centre.
View More Questions