4GMAT Diagnostic Test Q13 - Problem Solving - Number Properties
- 1. GMAT QUANTITATIVE REASONING NUMBER PROPERTIES PROBLEM SOLVING Diagnostic Test
- 2. Question A 2-digit positive integer ‘ab’ is written as ‘ba’, where a and b take values from 1 to 9, inclusive. The difference between ab and ba is 36. Which of the following could be the value of ab? I. 71 II. 62 III. 84 A. I only B. II only C. I and III only D. II and III only E. I, II and III
- 3. Method 1 – Best Method Back substitute answer choices
- 4. Choice I: 71 The difference between ab and ba is 36. I. 71 II. 62 III. 84 · If ab = 71, ba = 17
- 5. Choice I: 71 The difference between ab and ba is 36. I. 71 II. 62 III. 84 · If ab = 71, ba = 17 ab – ba = 71- 17 = 54
- 6. Choice I: 71 The difference between ab and ba is 36. I. 71 II. 62 III. 84 · If ab = 71, ba = 17 ab – ba = 71- 17 = 54
- 7. Choice I: 71 Choice II: 62 The difference between ab and ba is 36. I. 71 II. 62 III. 84 · If ab = 71, ba = 17 ab – ba = 71- 17 = 54 · If ab = 62, ba = 26
- 8. Choice I: 71 Choice II: 62 The difference between ab and ba is 36. I. 71 II. 62 III. 84 · If ab = 71, ba = 17 ab – ba = 71- 17 = 54 · If ab = 62, ba = 26 ab – ba = 62 - 26 = 36
- 9. Choice I: 71 Choice II: 62 The difference between ab and ba is 36. I. 71 II. 62 III. 84 · If ab = 71, ba = 17 ab – ba = 71- 17 = 54 · If ab = 62, ba = 26 ab – ba = 62 - 26 = 36
- 10. Choice III: 84Choice I: 71 Choice II: 62 The difference between ab and ba is 36. I. 71 II. 62 III. 84 · If ab = 71, ba = 17 ab – ba = 71- 17 = 54 · If ab = 84, ba = 48· If ab = 62, ba = 26 ab – ba = 62 - 26 = 36
- 11. Choice III: 84Choice I: 71 Choice II: 62 The difference between ab and ba is 36. I. 71 II. 62 III. 84 · If ab = 71, ba = 17 ab – ba = 71- 17 = 54 · If ab = 84, ba = 48 ab – ba = 84 - 48 = 36 · If ab = 62, ba = 26 ab – ba = 62 - 26 = 36
- 12. Choice III: 84Choice I: 71 Choice II: 62 The difference between ab and ba is 36. I. 71 II. 62 III. 84 · If ab = 71, ba = 17 ab – ba = 71- 17 = 54 · If ab = 84, ba = 48 ab – ba = 84 - 48 = 36 · If ab = 62, ba = 26 ab – ba = 62 - 26 = 36
- 13. Choice III: 84Choice I: 71 Choice II: 62 The difference between ab and ba is 36. I. 71 II. 62 III. 84 Options II and III · If ab = 71, ba = 17 ab – ba = 71- 17 = 54 · If ab = 84, ba = 48 ab – ba = 84 - 48 = 36 · If ab = 62, ba = 26 ab – ba = 62 - 26 = 36
- 14. Choice III: 84Choice I: 71 Choice II: 62 The difference between ab and ba is 36. I. 71 II. 62 III. 84 Correct Answer choice D. Options II and III · If ab = 71, ba = 17 ab – ba = 71- 17 = 54 · If ab = 84, ba = 48 ab – ba = 84 - 48 = 36 · If ab = 62, ba = 26 ab – ba = 62 - 26 = 36
- 15. Method 2 The theory behind the question
- 16. The difference between ab and ba is 36. I. 71 II. 62 III. 84 01 Theoretical approach to solving the question
- 17. The difference between ab and ba is 36. I. 71 II. 62 III. 84 01 Theoretical approach to solving the question · Any two digit number, say 43 can be written as 4*10 + 3*1
- 18. The difference between ab and ba is 36. I. 71 II. 62 III. 84 01 Theoretical approach to solving the question · Any two digit number, say 43 can be written as 4*10 + 3*1 So, ab can be written as a*10 + b*1 or 10a + b; a is the tens digit and b the is units digit.
- 19. The difference between ab and ba is 36. I. 71 II. 62 III. 84 01 Theoretical approach to solving the question · Any two digit number, say 43 can be written as 4*10 + 3*1 So, ab can be written as a*10 + b*1 or 10a + b; a is the tens digit and b the is units digit. And, ba can be written as b*10 + a*1 or 10b + a; b is the tens digit and a is the units digit.
- 20. The difference between ab and ba is 36. I. 71 II. 62 III. 84 01 Theoretical approach to solving the question · Any two digit number, say 43 can be written as 4*10 + 3*1 So, ab can be written as a*10 + b*1 or 10a + b; a is the tens digit and b the is units digit. And, ba can be written as b*10 + a*1 or 10b + a; b is the tens digit and a is the units digit. ab – ba = 10a + b – (10b + a) = 9(a – b)
- 21. The difference between ab and ba is 36. I. 71 II. 62 III. 84 01 Theoretical approach to solving the question · Any two digit number, say 43 can be written as 4*10 + 3*1 So, ab can be written as a*10 + b*1 or 10a + b; a is the tens digit and b the is units digit. And, ba can be written as b*10 + a*1 or 10b + a; b is the tens digit and a is the units digit. ab – ba = 10a + b – (10b + a) = 9(a – b) Question states ab – ba = 36·
- 22. The difference between ab and ba is 36. I. 71 II. 62 III. 84 01 Theoretical approach to solving the question · Any two digit number, say 43 can be written as 4*10 + 3*1 So, ab can be written as a*10 + b*1 or 10a + b; a is the tens digit and b the is units digit. And, ba can be written as b*10 + a*1 or 10b + a; b is the tens digit and a is the units digit. ab – ba = 10a + b – (10b + a) = 9(a – b) Question states ab – ba = 36· So, 9(a – b) = 36 or (a – b) = 4
- 23. The difference between ab and ba is 36. I. 71 II. 62 III. 84 01 Theoretical approach to solving the question · Any two digit number, say 43 can be written as 4*10 + 3*1 So, ab can be written as a*10 + b*1 or 10a + b; a is the tens digit and b the is units digit. And, ba can be written as b*10 + a*1 or 10b + a; b is the tens digit and a is the units digit. ab – ba = 10a + b – (10b + a) = 9(a – b) Question states ab – ba = 36· So, 9(a – b) = 36 or (a – b) = 4 i.e., the difference between the tens and units place of the number is 4. Check which choices match above criterion
- 24. The difference between ab and ba is 36. I. 71 II. 62 III. 84 01 Theoretical approach to solving the question · Any two digit number, say 43 can be written as 4*10 + 3*1 So, ab can be written as a*10 + b*1 or 10a + b; a is the tens digit and b the is units digit. And, ba can be written as b*10 + a*1 or 10b + a; b is the tens digit and a is the units digit. ab – ba = 10a + b – (10b + a) = 9(a – b) Question states ab – ba = 36· So, 9(a – b) = 36 or (a – b) = 4 i.e., the difference between the tens and units place of the number is 4. Check which choices match above criterion Choice I: 71. (7 – 1) ≠ 4
- 25. The difference between ab and ba is 36. I. 71 II. 62 III. 84 01 Theoretical approach to solving the question · Any two digit number, say 43 can be written as 4*10 + 3*1 So, ab can be written as a*10 + b*1 or 10a + b; a is the tens digit and b the is units digit. And, ba can be written as b*10 + a*1 or 10b + a; b is the tens digit and a is the units digit. ab – ba = 10a + b – (10b + a) = 9(a – b) Question states ab – ba = 36· So, 9(a – b) = 36 or (a – b) = 4 i.e., the difference between the tens and units place of the number is 4. Check which choices match above criterion Choice I: 71. (7 – 1) ≠ 4
- 26. The difference between ab and ba is 36. I. 71 II. 62 III. 84 01 Theoretical approach to solving the question · Any two digit number, say 43 can be written as 4*10 + 3*1 So, ab can be written as a*10 + b*1 or 10a + b; a is the tens digit and b the is units digit. And, ba can be written as b*10 + a*1 or 10b + a; b is the tens digit and a is the units digit. ab – ba = 10a + b – (10b + a) = 9(a – b) Question states ab – ba = 36· So, 9(a – b) = 36 or (a – b) = 4 i.e., the difference between the tens and units place of the number is 4. Check which choices match above criterion Choice I: 71. (7 – 1) ≠ 4 Choice II: 62. (6 – 2) = 4
- 27. The difference between ab and ba is 36. I. 71 II. 62 III. 84 01 Theoretical approach to solving the question · Any two digit number, say 43 can be written as 4*10 + 3*1 So, ab can be written as a*10 + b*1 or 10a + b; a is the tens digit and b the is units digit. And, ba can be written as b*10 + a*1 or 10b + a; b is the tens digit and a is the units digit. ab – ba = 10a + b – (10b + a) = 9(a – b) Question states ab – ba = 36· So, 9(a – b) = 36 or (a – b) = 4 i.e., the difference between the tens and units place of the number is 4. Check which choices match above criterion Choice I: 71. (7 – 1) ≠ 4 Choice II: 62. (6 – 2) = 4
- 28. The difference between ab and ba is 36. I. 71 II. 62 III. 84 01 Theoretical approach to solving the question · Any two digit number, say 43 can be written as 4*10 + 3*1 So, ab can be written as a*10 + b*1 or 10a + b; a is the tens digit and b the is units digit. And, ba can be written as b*10 + a*1 or 10b + a; b is the tens digit and a is the units digit. ab – ba = 10a + b – (10b + a) = 9(a – b) Question states ab – ba = 36· So, 9(a – b) = 36 or (a – b) = 4 i.e., the difference between the tens and units place of the number is 4. Check which choices match above criterion Choice I: 71. (7 – 1) ≠ 4 Choice II: 62. (6 – 2) = 4 Choice III: 84. (8 – 4) = 4
- 29. The difference between ab and ba is 36. I. 71 II. 62 III. 84 01 Theoretical approach to solving the question · Any two digit number, say 43 can be written as 4*10 + 3*1 So, ab can be written as a*10 + b*1 or 10a + b; a is the tens digit and b the is units digit. And, ba can be written as b*10 + a*1 or 10b + a; b is the tens digit and a is the units digit. ab – ba = 10a + b – (10b + a) = 9(a – b) Question states ab – ba = 36· So, 9(a – b) = 36 or (a – b) = 4 i.e., the difference between the tens and units place of the number is 4. Check which choices match above criterion Choice I: 71. (7 – 1) ≠ 4 Choice II: 62. (6 – 2) = 4 Choice III: 84. (8 – 4) = 4
- 31. Difference between ‘ab’ and ‘ba’; Sum of ‘ab’ and ‘ba’ For any two digit number ab, the difference between ab and ba (ab – ba) is always = 9(a – b)
- 32. Difference between ‘ab’ and ‘ba’; Sum of ‘ab’ and ‘ba’ For any two digit number ab, the difference between ab and ba (ab – ba) is always = 9(a – b) Similarly, for any two digit number ab, the sum of ab and ba (ab + ba) is always = 11(a + b)
- 33. For GMAT Prep Visit http://www.4gmat.com GMAT Classes and GMAT Preparation Send your comments / feedback to info@4gmat.com
- 34. 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