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What is the greatest number of markers

This topic has 1 expert reply and 0 member replies

What is the greatest number of markers

Post Fri Sep 15, 2017 7:37 pm
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    What is the greatest number of markers that can be purchased for $18?

    (1) 4 markers or 6 pens or 12 pencils can be purchased for $36

    (2) If the cost of each marker is increased by $3, 5 less markers can be purchased for $180

    The OA is D.

    Really statement (2) alone is sufficient? Can anyone explain it to me.

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    Post Sat Sep 16, 2017 3:50 am
    Vincen wrote:
    What is the greatest number of markers that can be purchased for $18?

    (1) 4 markers or 6 pens or 12 pencils can be purchased for $36

    (2) If the cost of each marker is increased by $3, 5 less markers can be purchased for $180

    The OA is D.

    Really statement (2) alone is sufficient? Can anyone explain it to me.
    Hi Vincen,

    Yes, Statement 2 itself is also sufficient.

    Say the price of a marker is $x. Thus, in $180, one can buy 180/x numbers of markers.

    Given that the new price is $(x+3), one would buy five fewer markers than before.

    Thus,

    Number of markers before = Number of markers after + 5

    180/x = 180/(x + 3) + 5

    => 180/x - 180/(x + 3) = 5

    180[{(x+3) - x}/x(x+3)] = 5

    36[{x + 3 - x}/x(x+3)] = 1; '180' is camcelled by '5.'

    36[3/x(x+3)] = 1

    x(x + 3) = 36 x 3

    x(x + 3) = 12 x 3 x 3

    x(x + 3) = 9 x 12

    => x = $9

    Thus, one can buy $18/$9 = 2 numbers of markers. Sufficient.

    Hope this helps!

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    Thanked by: Vincen

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