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Manager
Joined: 08 Apr 2004
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The numbers x and y are threedigit positive integers, and x
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27 Aug 2004, 06:22
Question Stats:
68% (02:10) correct 32% (02:30) wrong based on 336 sessions
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The numbers x and y are threedigit positive integers, and x + y is a fourdigit 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
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Re: The numbers x and y are threedigit positive integers, and x
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27 Aug 2004, 07:07
marine wrote: The numbers x and y are threedigit positive integers, and x + y is a fourdigit 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.
Am I getting something wrong here??



Manager
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Re: The numbers x and y are threedigit positive integers, and x
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27 Aug 2004, 07:28
I believe the answer is B
If the hundred is less than 5 it is not possible to get 4 digits for x + y.
example:
y = 459 (highest possible with hundred digit 4.
x = 379 (highest possible when y has hundred digit 4).
x + y = 838
Correct me if I am wrong.
Regards,
Alex



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Re: The numbers x and y are threedigit positive integers, and x
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27 Aug 2004, 07:38
B. III Only.
Let Xh = hundredth digit of X. Xd = tenth digit of X. Similarly Yh and Yt for Y.
To get a sum of four digits from two three digit numbers, Xh+Yh should be >=10
You get a carry over of "1" from Xt+Yt (7+5="1"2)
S0, Xh+Yh >=9
Given that X<Y, Xhhas to be lesser than Yh, because the tenth digit of X (7) is greater than that of Y(5))
Hence, Y has to be >=5
For eg: Y=5, X=4  Correct
OR Y=6, X=3  Correct
OR Y=4, X=3  Wrong



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Re: The numbers x and y are threedigit positive integers, and x
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27 Aug 2004, 08:31
my guess is E
x=475 and y=550
x+y=1025 ..it satisfy 2nd and 3rd statement..
otherwise if we look into stem it says x's tens digit should be 7 and y's 5 if we add it should always be 2 (7+5=12)



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Re: The numbers x and y are threedigit positive integers, and x
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27 Aug 2004, 11:35
Neelam,
The tens digit of x + y doesnt have to be 2.
It can equal 2 but also it can equal 3. Therefore is not that it must be true.
Example:
x = 478, y = 559, x + y = 1037
x = 475, y = 550, x + y = 1025
Regards,
Alex



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Re: The numbers x and y are threedigit positive integers, and x
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08 Feb 2016, 18:04
marine wrote: The numbers x and y are threedigit positive integers, and x + y is a fourdigit 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 we can easily arrive to the answer choices if we give values to x and y: x=879 y=959 I we can see that units digit of x+y is less than units digit of either one. we can eliminate C and D right away. II again, we can add 879+959  and the tens digit is not 2.  we can eliminate A and E, and pick up E.



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Re: The numbers x and y are threedigit positive integers, and x
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10 Feb 2019, 08:47
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Re: The numbers x and y are threedigit positive integers, and x
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10 Feb 2019, 08:47






