ºÝºÝߣ

ºÝºÝߣShare a Scribd company logo

4GMAT Diagnostic Test Q1 - Problem Solving : Number Properties HCF

•
•
4
4gmatprep

This question appeared as part of 4GMAT's GMAT diagnostic test. This one is a problem solving question in arithmetic. It is from the topic Number Properties and tests your understanding of HCF. A bag contains 72 red marbles, 45 green marbles and 108 blue marbles. These are packed into packets containing equal number of marbles of the same colour. What is minimum number of packets required? A) 9 B) 36 C) 25 D) 19 E) 21

1 of 42
Downloaded 17 times
GMAT QUANTITATIVE REASONING NUMBER PROPERTIES : HCF PROBLEM SOLVING Diagnostic Test
Question A bag contains 72 red marbles, 45 green marbles and 108 blue marbles. These are packed into packets containing equal number of marbles of the same colour. What is minimum number of packets required? A. 9 B. 36 C. 25 D. 19 E. 21
Step 1 Decoding the information given
What is minimum number of packets required? 72 red marbles, 45 green marbles and 108 blue marbles. Idea #1
What is minimum number of packets required? 72 red marbles, 45 green marbles and 108 blue marbles. Idea #1 Packed into packets containing equal number of marbles of the same color.
What is minimum number of packets required? 72 red marbles, 45 green marbles and 108 blue marbles. Idea #1 Packed into packets containing equal number of marbles of the same color. Equal Number in Each Packet
What is minimum number of packets required? 72 red marbles, 45 green marbles and 108 blue marbles. Idea #1 Packed into packets containing equal number of marbles of the same color. Equal Number in Each Packet Number of marbles in all the packets is the same. Let us say the number is ‘n’
What is minimum number of packets required? 72 red marbles, 45 green marbles and 108 blue marbles. Idea #1 Packed into packets containing equal number of marbles of the same color. Equal Number in Each Packet Same color Number of marbles in all the packets is the same. Let us say the number is ‘n’
What is minimum number of packets required? 72 red marbles, 45 green marbles and 108 blue marbles. Idea #1 Packed into packets containing equal number of marbles of the same color. Equal Number in Each Packet All ‘n’ marbles in a packet should be of the same colour Same color Number of marbles in all the packets is the same. Let us say the number is ‘n’
What is minimum number of packets required? 72 red marbles, 45 green marbles and 108 blue marbles. Idea #1 Packed into packets containing equal number of marbles of the same color. Equal Number in Each Packet All ‘n’ marbles in a packet should be of the same colour Same color What does it translate into? Number of marbles in all the packets is the same. Let us say the number is ‘n’
What is minimum number of packets required? 72 red marbles, 45 green marbles and 108 blue marbles. Idea #1 Packed into packets containing equal number of marbles of the same color. Equal Number in Each Packet All ‘n’ marbles in a packet should be of the same colour Same color What does it translate into? ‘n’ should be a factor of 72 if all red marbles are to be packed into packets containing ‘n’ marbles. Number of marbles in all the packets is the same. Let us say the number is ‘n’
What is minimum number of packets required? 72 red marbles, 45 green marbles and 108 blue marbles. Idea #1 Packed into packets containing equal number of marbles of the same color. Equal Number in Each Packet All ‘n’ marbles in a packet should be of the same colour Same color What does it translate into? ‘n’ should be a factor of 72 if all red marbles are to be packed into packets containing ‘n’ marbles. By the same token, n should be a factor of 45 and 108 as well. Number of marbles in all the packets is the same. Let us say the number is ‘n’
What is minimum number of packets required? 72 red marbles, 45 green marbles and 108 blue marbles. Idea #1 Packed into packets containing equal number of marbles of the same color. Equal Number in Each Packet All ‘n’ marbles in a packet should be of the same colour Same color What does it translate into? ‘n’ should be a factor of 72 if all red marbles are to be packed into packets containing ‘n’ marbles. By the same token, n should be a factor of 45 and 108 as well. ‘n’ is a common factor of 72, 45 and 108. Number of marbles in all the packets is the same. Let us say the number is ‘n’
72 red marbles, 45 green marbles and 108 blue marbles. What is minimum number of packets required? Idea #2
72 red marbles, 45 green marbles and 108 blue marbles. What is minimum number of packets required? Idea #2 What is the minimum number of packets required?
72 red marbles, 45 green marbles and 108 blue marbles. What is minimum number of packets required? Idea #2 What is the minimum number of packets required? Number of packets - MINIMUM
72 red marbles, 45 green marbles and 108 blue marbles. What is minimum number of packets required? Idea #2 What is the minimum number of packets required? Number of packets - MINIMUM More the number of marbles in each packet, lesser the number of packets. i.e., maximize ‘n’ to minimize number of packets.
72 red marbles, 45 green marbles and 108 blue marbles. What is minimum number of packets required? Idea #2 What is the minimum number of packets required? Number of packets - MINIMUM More the number of marbles in each packet, lesser the number of packets. i.e., maximize ‘n’ to minimize number of packets. ‘n’ is a common factor
72 red marbles, 45 green marbles and 108 blue marbles. What is minimum number of packets required? Idea #2 What is the minimum number of packets required? Number of packets - MINIMUM More the number of marbles in each packet, lesser the number of packets. i.e., maximize ‘n’ to minimize number of packets. We determined that ‘n’ is a factor common to 72, 45, and 108 ‘n’ is a common factor
72 red marbles, 45 green marbles and 108 blue marbles. What is minimum number of packets required? Idea #2 What is the minimum number of packets required? Number of packets - MINIMUM More the number of marbles in each packet, lesser the number of packets. i.e., maximize ‘n’ to minimize number of packets. We determined that ‘n’ is a factor common to 72, 45, and 108 ‘n’ is a common factor Combining findings above
72 red marbles, 45 green marbles and 108 blue marbles. What is minimum number of packets required? Idea #2 What is the minimum number of packets required? Number of packets - MINIMUM More the number of marbles in each packet, lesser the number of packets. i.e., maximize ‘n’ to minimize number of packets. We determined that ‘n’ is a factor common to 72, 45, and 108 ‘n’ is a common factor Combining findings above ‘n’ should be a common factor of 72, 45, and 108 and ‘n’ has to be as high as possible.
72 red marbles, 45 green marbles and 108 blue marbles. What is minimum number of packets required? Idea #2 What is the minimum number of packets required? Number of packets - MINIMUM More the number of marbles in each packet, lesser the number of packets. i.e., maximize ‘n’ to minimize number of packets. We determined that ‘n’ is a factor common to 72, 45, and 108 ‘n’ is a common factor Combining findings above ‘n’ should be a common factor of 72, 45, and 108 and ‘n’ has to be as high as possible. ‘n’ is the highest common factor (HCF) of 72, 45 and 108.
Step 2 How to compute HCF?
72 red marbles, 45 green marbles and 108 blue marbles. What is minimum number of packets required? Prime Factorization Method
72 red marbles, 45 green marbles and 108 blue marbles. What is minimum number of packets required? Prime Factorization Method STEP 01 Prime factorize the 3 numbers
72 red marbles, 45 green marbles and 108 blue marbles. What is minimum number of packets required? Prime Factorization Method STEP 01 Prime factorize the 3 numbers 72 = 23 * 32
72 red marbles, 45 green marbles and 108 blue marbles. What is minimum number of packets required? Prime Factorization Method STEP 01 Prime factorize the 3 numbers 72 = 23 * 32 45 = 32 * 5
72 red marbles, 45 green marbles and 108 blue marbles. What is minimum number of packets required? Prime Factorization Method STEP 01 Prime factorize the 3 numbers 72 = 23 * 32 45 = 32 * 5 108 = 22 * 33
72 red marbles, 45 green marbles and 108 blue marbles. What is minimum number of packets required? Prime Factorization Method STEP 01 Prime factorize the 3 numbers 72 = 23 * 32 45 = 32 * 5 108 = 22 * 33 STEP 02 List down prime factors common to all the numbers
72 red marbles, 45 green marbles and 108 blue marbles. What is minimum number of packets required? Prime Factorization Method STEP 01 Prime factorize the 3 numbers 72 = 23 * 32 45 = 32 * 5 108 = 22 * 33 STEP 02 List down prime factors common to all the numbers
72 red marbles, 45 green marbles and 108 blue marbles. What is minimum number of packets required? Prime Factorization Method STEP 01 Prime factorize the 3 numbers 72 = 23 * 32 45 = 32 * 5 108 = 22 * 33 STEP 02 List down prime factors common to all the numbers 3 is the only prime factor common to all the numbers
72 red marbles, 45 green marbles and 108 blue marbles. What is minimum number of packets required? Prime Factorization Method STEP 01 Prime factorize the 3 numbers 72 = 23 * 32 45 = 32 * 5 108 = 22 * 33 STEP 02 List down prime factors common to all the numbers 3 is the only prime factor common to all the numbers Pick the lowest power of the prime factors common to all numbers and multiply to get the HCF STEP 03
72 red marbles, 45 green marbles and 108 blue marbles. What is minimum number of packets required? Prime Factorization Method STEP 01 Prime factorize the 3 numbers 72 = 23 * 32 45 = 32 * 5 108 = 22 * 33 STEP 02 List down prime factors common to all the numbers 3 is the only prime factor common to all the numbers Pick the lowest power of the prime factors common to all numbers and multiply to get the HCF The lowest power of the only common factor ‘3’ is 32 STEP 03
72 red marbles, 45 green marbles and 108 blue marbles. What is minimum number of packets required? Prime Factorization Method STEP 01 Prime factorize the 3 numbers 72 = 23 * 32 45 = 32 * 5 108 = 22 * 33 STEP 02 List down prime factors common to all the numbers 3 is the only prime factor common to all the numbers Pick the lowest power of the prime factors common to all numbers and multiply to get the HCF The lowest power of the only common factor ‘3’ is 32 The HCF is 32 = 9 STEP 03
It’s far from over We have to compute the number of packets – not the number of marbles in each packet
72 red marbles, 45 green marbles and 108 blue marbles. What is minimum number of packets required? Number of marbles in each packet = 9
72 red marbles, 45 green marbles and 108 blue marbles. What is minimum number of packets required? Number of marbles in each packet = 9 72 red marbles can therefore, be packed into 8 packets.
72 red marbles, 45 green marbles and 108 blue marbles. What is minimum number of packets required? Number of marbles in each packet = 9 72 red marbles can therefore, be packed into 8 packets. 45 green marbles can be packed into 5 packets.
72 red marbles, 45 green marbles and 108 blue marbles. What is minimum number of packets required? Number of marbles in each packet = 9 72 red marbles can therefore, be packed into 8 packets. 45 green marbles can be packed into 5 packets. 108 blue marbles can be packed into 12 packets.
72 red marbles, 45 green marbles and 108 blue marbles. Total number of packets = 8 + 5 + 12 = 25 packets What is minimum number of packets required? Number of marbles in each packet = 9 72 red marbles can therefore, be packed into 8 packets. 45 green marbles can be packed into 5 packets. 108 blue marbles can be packed into 12 packets.
72 red marbles, 45 green marbles and 108 blue marbles. Total number of packets = 8 + 5 + 12 = 25 packets What is minimum number of packets required? Number of marbles in each packet = 9 72 red marbles can therefore, be packed into 8 packets. 45 green marbles can be packed into 5 packets. 108 blue marbles can be packed into 12 packets. Choice C is the correct answer
4GMAT We offer classroom training in Chennai and Bangalore Tutors include GMAT 98%ilers, US B School graduates and IIM graduates Call us: +91 95000 48484 Mail us: info@4gmat.com

More Related Content

4GMAT Diagnostic Test Q1 - Problem Solving : Number Properties HCF

  • 1. GMAT QUANTITATIVE REASONING NUMBER PROPERTIES : HCF PROBLEM SOLVING Diagnostic Test
  • 2. Question A bag contains 72 red marbles, 45 green marbles and 108 blue marbles. These are packed into packets containing equal number of marbles of the same colour. What is minimum number of packets required? A. 9 B. 36 C. 25 D. 19 E. 21
  • 3. Step 1 Decoding the information given
  • 4. What is minimum number of packets required? 72 red marbles, 45 green marbles and 108 blue marbles. Idea #1
  • 5. What is minimum number of packets required? 72 red marbles, 45 green marbles and 108 blue marbles. Idea #1 Packed into packets containing equal number of marbles of the same color.
  • 6. What is minimum number of packets required? 72 red marbles, 45 green marbles and 108 blue marbles. Idea #1 Packed into packets containing equal number of marbles of the same color. Equal Number in Each Packet
  • 7. What is minimum number of packets required? 72 red marbles, 45 green marbles and 108 blue marbles. Idea #1 Packed into packets containing equal number of marbles of the same color. Equal Number in Each Packet Number of marbles in all the packets is the same. Let us say the number is ‘n’
  • 8. What is minimum number of packets required? 72 red marbles, 45 green marbles and 108 blue marbles. Idea #1 Packed into packets containing equal number of marbles of the same color. Equal Number in Each Packet Same color Number of marbles in all the packets is the same. Let us say the number is ‘n’
  • 9. What is minimum number of packets required? 72 red marbles, 45 green marbles and 108 blue marbles. Idea #1 Packed into packets containing equal number of marbles of the same color. Equal Number in Each Packet All ‘n’ marbles in a packet should be of the same colour Same color Number of marbles in all the packets is the same. Let us say the number is ‘n’
  • 10. What is minimum number of packets required? 72 red marbles, 45 green marbles and 108 blue marbles. Idea #1 Packed into packets containing equal number of marbles of the same color. Equal Number in Each Packet All ‘n’ marbles in a packet should be of the same colour Same color What does it translate into? Number of marbles in all the packets is the same. Let us say the number is ‘n’
  • 11. What is minimum number of packets required? 72 red marbles, 45 green marbles and 108 blue marbles. Idea #1 Packed into packets containing equal number of marbles of the same color. Equal Number in Each Packet All ‘n’ marbles in a packet should be of the same colour Same color What does it translate into? ‘n’ should be a factor of 72 if all red marbles are to be packed into packets containing ‘n’ marbles. Number of marbles in all the packets is the same. Let us say the number is ‘n’
  • 12. What is minimum number of packets required? 72 red marbles, 45 green marbles and 108 blue marbles. Idea #1 Packed into packets containing equal number of marbles of the same color. Equal Number in Each Packet All ‘n’ marbles in a packet should be of the same colour Same color What does it translate into? ‘n’ should be a factor of 72 if all red marbles are to be packed into packets containing ‘n’ marbles. By the same token, n should be a factor of 45 and 108 as well. Number of marbles in all the packets is the same. Let us say the number is ‘n’
  • 13. What is minimum number of packets required? 72 red marbles, 45 green marbles and 108 blue marbles. Idea #1 Packed into packets containing equal number of marbles of the same color. Equal Number in Each Packet All ‘n’ marbles in a packet should be of the same colour Same color What does it translate into? ‘n’ should be a factor of 72 if all red marbles are to be packed into packets containing ‘n’ marbles. By the same token, n should be a factor of 45 and 108 as well. ‘n’ is a common factor of 72, 45 and 108. Number of marbles in all the packets is the same. Let us say the number is ‘n’
  • 14. 72 red marbles, 45 green marbles and 108 blue marbles. What is minimum number of packets required? Idea #2
  • 15. 72 red marbles, 45 green marbles and 108 blue marbles. What is minimum number of packets required? Idea #2 What is the minimum number of packets required?
  • 16. 72 red marbles, 45 green marbles and 108 blue marbles. What is minimum number of packets required? Idea #2 What is the minimum number of packets required? Number of packets - MINIMUM
  • 17. 72 red marbles, 45 green marbles and 108 blue marbles. What is minimum number of packets required? Idea #2 What is the minimum number of packets required? Number of packets - MINIMUM More the number of marbles in each packet, lesser the number of packets. i.e., maximize ‘n’ to minimize number of packets.
  • 18. 72 red marbles, 45 green marbles and 108 blue marbles. What is minimum number of packets required? Idea #2 What is the minimum number of packets required? Number of packets - MINIMUM More the number of marbles in each packet, lesser the number of packets. i.e., maximize ‘n’ to minimize number of packets. ‘n’ is a common factor
  • 19. 72 red marbles, 45 green marbles and 108 blue marbles. What is minimum number of packets required? Idea #2 What is the minimum number of packets required? Number of packets - MINIMUM More the number of marbles in each packet, lesser the number of packets. i.e., maximize ‘n’ to minimize number of packets. We determined that ‘n’ is a factor common to 72, 45, and 108 ‘n’ is a common factor
  • 20. 72 red marbles, 45 green marbles and 108 blue marbles. What is minimum number of packets required? Idea #2 What is the minimum number of packets required? Number of packets - MINIMUM More the number of marbles in each packet, lesser the number of packets. i.e., maximize ‘n’ to minimize number of packets. We determined that ‘n’ is a factor common to 72, 45, and 108 ‘n’ is a common factor Combining findings above
  • 21. 72 red marbles, 45 green marbles and 108 blue marbles. What is minimum number of packets required? Idea #2 What is the minimum number of packets required? Number of packets - MINIMUM More the number of marbles in each packet, lesser the number of packets. i.e., maximize ‘n’ to minimize number of packets. We determined that ‘n’ is a factor common to 72, 45, and 108 ‘n’ is a common factor Combining findings above ‘n’ should be a common factor of 72, 45, and 108 and ‘n’ has to be as high as possible.
  • 22. 72 red marbles, 45 green marbles and 108 blue marbles. What is minimum number of packets required? Idea #2 What is the minimum number of packets required? Number of packets - MINIMUM More the number of marbles in each packet, lesser the number of packets. i.e., maximize ‘n’ to minimize number of packets. We determined that ‘n’ is a factor common to 72, 45, and 108 ‘n’ is a common factor Combining findings above ‘n’ should be a common factor of 72, 45, and 108 and ‘n’ has to be as high as possible. ‘n’ is the highest common factor (HCF) of 72, 45 and 108.
  • 23. Step 2 How to compute HCF?
  • 24. 72 red marbles, 45 green marbles and 108 blue marbles. What is minimum number of packets required? Prime Factorization Method
  • 25. 72 red marbles, 45 green marbles and 108 blue marbles. What is minimum number of packets required? Prime Factorization Method STEP 01 Prime factorize the 3 numbers
  • 26. 72 red marbles, 45 green marbles and 108 blue marbles. What is minimum number of packets required? Prime Factorization Method STEP 01 Prime factorize the 3 numbers 72 = 23 * 32
  • 27. 72 red marbles, 45 green marbles and 108 blue marbles. What is minimum number of packets required? Prime Factorization Method STEP 01 Prime factorize the 3 numbers 72 = 23 * 32 45 = 32 * 5
  • 28. 72 red marbles, 45 green marbles and 108 blue marbles. What is minimum number of packets required? Prime Factorization Method STEP 01 Prime factorize the 3 numbers 72 = 23 * 32 45 = 32 * 5 108 = 22 * 33
  • 29. 72 red marbles, 45 green marbles and 108 blue marbles. What is minimum number of packets required? Prime Factorization Method STEP 01 Prime factorize the 3 numbers 72 = 23 * 32 45 = 32 * 5 108 = 22 * 33 STEP 02 List down prime factors common to all the numbers
  • 30. 72 red marbles, 45 green marbles and 108 blue marbles. What is minimum number of packets required? Prime Factorization Method STEP 01 Prime factorize the 3 numbers 72 = 23 * 32 45 = 32 * 5 108 = 22 * 33 STEP 02 List down prime factors common to all the numbers
  • 31. 72 red marbles, 45 green marbles and 108 blue marbles. What is minimum number of packets required? Prime Factorization Method STEP 01 Prime factorize the 3 numbers 72 = 23 * 32 45 = 32 * 5 108 = 22 * 33 STEP 02 List down prime factors common to all the numbers 3 is the only prime factor common to all the numbers
  • 32. 72 red marbles, 45 green marbles and 108 blue marbles. What is minimum number of packets required? Prime Factorization Method STEP 01 Prime factorize the 3 numbers 72 = 23 * 32 45 = 32 * 5 108 = 22 * 33 STEP 02 List down prime factors common to all the numbers 3 is the only prime factor common to all the numbers Pick the lowest power of the prime factors common to all numbers and multiply to get the HCF STEP 03
  • 33. 72 red marbles, 45 green marbles and 108 blue marbles. What is minimum number of packets required? Prime Factorization Method STEP 01 Prime factorize the 3 numbers 72 = 23 * 32 45 = 32 * 5 108 = 22 * 33 STEP 02 List down prime factors common to all the numbers 3 is the only prime factor common to all the numbers Pick the lowest power of the prime factors common to all numbers and multiply to get the HCF The lowest power of the only common factor ‘3’ is 32 STEP 03
  • 34. 72 red marbles, 45 green marbles and 108 blue marbles. What is minimum number of packets required? Prime Factorization Method STEP 01 Prime factorize the 3 numbers 72 = 23 * 32 45 = 32 * 5 108 = 22 * 33 STEP 02 List down prime factors common to all the numbers 3 is the only prime factor common to all the numbers Pick the lowest power of the prime factors common to all numbers and multiply to get the HCF The lowest power of the only common factor ‘3’ is 32 The HCF is 32 = 9 STEP 03
  • 35. It’s far from over We have to compute the number of packets – not the number of marbles in each packet
  • 36. 72 red marbles, 45 green marbles and 108 blue marbles. What is minimum number of packets required? Number of marbles in each packet = 9
  • 37. 72 red marbles, 45 green marbles and 108 blue marbles. What is minimum number of packets required? Number of marbles in each packet = 9 72 red marbles can therefore, be packed into 8 packets.
  • 38. 72 red marbles, 45 green marbles and 108 blue marbles. What is minimum number of packets required? Number of marbles in each packet = 9 72 red marbles can therefore, be packed into 8 packets. 45 green marbles can be packed into 5 packets.
  • 39. 72 red marbles, 45 green marbles and 108 blue marbles. What is minimum number of packets required? Number of marbles in each packet = 9 72 red marbles can therefore, be packed into 8 packets. 45 green marbles can be packed into 5 packets. 108 blue marbles can be packed into 12 packets.
  • 40. 72 red marbles, 45 green marbles and 108 blue marbles. Total number of packets = 8 + 5 + 12 = 25 packets What is minimum number of packets required? Number of marbles in each packet = 9 72 red marbles can therefore, be packed into 8 packets. 45 green marbles can be packed into 5 packets. 108 blue marbles can be packed into 12 packets.
  • 41. 72 red marbles, 45 green marbles and 108 blue marbles. Total number of packets = 8 + 5 + 12 = 25 packets What is minimum number of packets required? Number of marbles in each packet = 9 72 red marbles can therefore, be packed into 8 packets. 45 green marbles can be packed into 5 packets. 108 blue marbles can be packed into 12 packets. Choice C is the correct answer
  • 42. 4GMAT We offer classroom training in Chennai and Bangalore Tutors include GMAT 98%ilers, US B School graduates and IIM graduates Call us: +91 95000 48484 Mail us: info@4gmat.com