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How Many 3 Digit Numbers with Equal Two Digits?

Discussion in 'CAT/MAT/GMAT Preparation' started by Royaluni, Sep 12, 2015.

  1. Royaluni

    Royaluni Administrator

    GMAT Practice Question– of the three digit-integers greater than 700, how many have two digits that are equal to each other and the remaining digit different from the other two?

    A. 90

    B. 82

    C. 80

    D. 45

    E. 36

    Answer- so we need to find the number of 3 digit number between 700-1000 excluding 700 & 1000.

    Now we need to approach this problem, step by step;

    Step 1- total number of digit=999-700=299

    Step 2- these are 3 digit numbers and we need to identify the possibilities where 2 of these 3 digits are same like 771. Now we will see if there are any three digit numbers with all 3 same digits.

    There are total 3 such numbers

    777,888,999

    So out of 299

    3 are with all 3 same digits

    Next we can divide each 100 (701-800) in the 10 batch of 10 digits like;

    701-710

    711-720

    And so on till 800

    Same with 800-900 and 900-999

    If you do that, you will notice, each of these batch of 10 numbers will have 1 number when two numbers will be same like 711,722.

    Starting from 711 because first 10 numbers will contain 0, so starting from 711, you will get one number in each 10 number batch when two digits will be same, total of 8 numbers from 711 to 799;

    1. 711

    2. 722

    3. 733

    4. 744

    5. 755

    6. 766

    7. 788

    8. 799

    Now the next pattern is when a 3 digit number will have 2 same numbers but not adjacent to each other like;

    9. 707

    10. 717

    11. 727

    12. 737

    13. 747

    14. 757

    15. 767

    16. 787

    17. 797

    Now if you look at the serial number, we already have 17 numbers between 701 to 799. So far we have covered left two numbers at tens and ones position along with hundreds and ones positions.

    Now we will focus on hundreds and tens position;

    18. 770

    19. 771

    20. 772

    21. 773

    22. 774

    23. 775

    24. 776

    25. 778

    26. 779

    Similarly, you can count numbers with same two digits between 800-900 and 900-999. They will be same with one difference, 800 and 900 will be part of the calculation whereas 700 was left out of the calculation because question was asking for numbers “greater than 700”.


    So to calculate total number, we can multiply 26 * 3 + 2 = 80.

    Answer choice – C.

    Source- GMAT Official Guide 2016


    You can find similar maths problem in Quantitative section of other competitive exams also.

    What is the sum of the angles?
     

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