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In a three-digit number n, the hundreds digit is 3 times the

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Carcass
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In a three-digit number n, the hundreds digit is 3 times the [#permalink] New post   25 Dec 2018, 10:48
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In a three-digit number n, the hundreds digit is 3 times the units digit.

Quantity A
Quantity B
The units digit of n
4


A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
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B
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GreenlightTestPrep
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Re: In a three-digit number n, the hundreds digit is 3 times the [#permalink] New post   16 Dec 2019, 08:23
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Carcass wrote:


In a three-digit number n, the hundreds digit is 3 times the units digit.

Quantity A
Quantity B
The units digit of n
4


A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.


GIVEN: In a three-digit number n, the hundreds digit is 3 times the units digit.
There are only three possible cases in which the hundreds digit is three times the unit's digit:
Case i: the number is in the form: 3_1
Case ii: the number is in the form: 6_2
Case iii: the number is in the form: 9_3

Notice that, if the units digit is greater than 3, then the tens digit will be a TWO-DIGIT number, which is impossible.

We have:
QUANTITY A: 1, 2, or 3
QUANTITY B: 4

In all possible cases, Quantity B is greater

Answer: B

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Re: In a three-digit number n, the hundreds digit is 3 times the [#permalink] New post   21 Dec 2019, 21:16
The hundredth digit can only be 1,2,3 units digit can only be 3,6,9.

hence answer B
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In a three-digit number n, the hundreds digit is 3 times the [#permalink] New post   19 Jan 2024, 20:28
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Let a-b-c be the three digit number.

It can be rewritten as 3c-b-c

for

c=0,3c=0
c=1,3c=3
c=2,3c=6
c=3,3c=9
c=4,3c=12

The units digits of a-b-c, c, can only take the values 1,2,3 for if c=0 and consequently 3c=0, it is not a three digit number. If c=4, then the hundreds digit 3c = 12 which does not make sense.

Quantity A = 1,2, or 3
Quantity B = 4

Quantity B is always greater.
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In a three-digit number n, the hundreds digit is 3 times the [#permalink]
19 Jan 2024, 20:28
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