LUANDATO wrote:Scott and Jeff both purchased tickets to a certain play. If they both paid the same price per ticket and each purchased more than one ticket, how many tickets did Scott purchase? (Assume each ticket costs a whole number of dollars that is more than $1.)
(1) Jeff purchased $143 worth of tickets.
(2) Scott purchased $187 worth of tickets.
The OA is C.
Can any expert help me with this DS question please? I don't have it clear. Thanks.
Say the price of a ticket is $p, Scott purchased s tickets and Jeff purchased j tickets; where s, j, and p > 1
(1) Jeff purchased $143 worth of tickets.
We do not have any information about Scott. Insufficient.
(2) Scott purchased $187 worth of tickets.Â
=> s*p = 187
=> sp = 1*187 = 11*17
Since neither s nor p can be 1, we discard sp = 1*187. Thus, sp = 11*17
Since 11 and 17 are prime numbers, no further factorization is possible. But s can be either 11 or 17. No unique answer. Insufficient.
(1) and (2) combined:
Let's look at Statement 1 again. We know that Jeff purchased $143 worth of tickets.
=> j*p = 143
=> jp = 1*143 = 11*13
Since neither j nor p can be 1, we discard jp = 1*143. Thus, jp = 11*13
Since 11 and 13 are prime numbers, no further factorization is possible. j can be either 11 or 13.
Since jp = 11*13 and sp = 11*17, the common value is 11 and that can be the value of p. Thus, p = 11. Since p = 11, from sp = 11*17, we have s = 17. A unique answer. Scott purchase 17 tickets. Sufficient.
The correct answer:
C
Hope this helps!
-Jay
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