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The numbers x and y are three-digit positive integers, and x [#permalink]
27 Aug 2004, 06:22

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Difficulty:

45% (medium)

Question Stats:

57% (02:28) correct
43% (01:40) wrong based on 21 sessions

The numbers x and y are three-digit positive integers, and x + y is a four-digit integer. The tens digit of x equals 7 and the tens digit of y equals 5. If x < y, which of the following must be true?

I. The units digit of x + y is greater than the units digit of either x or y. II. The tens digit of x + y equals 2. III. The hundreds digit of y is at least 5.

A. II only B. III only C. I and II D. I and III E. II and III

Re: The numbers x and y are three-digit positive integers, and x [#permalink]
27 Aug 2004, 07:07

marine wrote:

The numbers x and y are three-digit positive integers, and x + y is a four-digit integer. The tens digit of x equals 7 and the tens digit of y equals 5. If x < y, which of the following must be true?

I. The units digit of x + y is greater than the units digit of either x or y. II. The tens digit of x + y equals 2. III. The hundreds digit of y is at least 5.

A. II only B. III only C. I and II D. I and III E. II and III

I. Not true: eg. 5+6 = 11 and 1< 5 or 6
II. Not true: if units digit sum is > 10, then tens digit = 3
III Not true: x+y needs to be greater than 999 and smaller than 1999. If y hundreds unit =5, x will be <5, and only if hundreds units of x is =, then x+ will have four digits. If x=3,2 or 1, then x+y will have three digits.

If III. were "The hundreds digit of x is at least 5" or the stem said "x>y" then III would be true.

Re: The numbers x and y are three-digit positive integers, and x [#permalink]
05 Oct 2014, 08:17

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