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655-705 Level|   Algebra|      
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Bunuel
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The digit in the units place of a number is equal to the digit in the 02 Aug 2021, 08:45
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55% (hard)

Question Stats:

64% (02:08) correct 36% (02:36) wrong based on 117 sessions

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The digit in the units place of a number is equal to the digit in the tens place of half of that number and the digit in the tens place of that number is less than the digit in units place of half of the number by 1. If the sum of the digits of the number is seven, then what is the number?

(A) 52
(B) 34
(C) 16
(D) 15
(E) 14
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A
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rajatchopra1994
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The digit in the units place of a number is equal to the digit in the 02 Aug 2021, 09:00
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Explanation:

(10x+y)/2 =10y + (x+1)
10x + y = 20y + 2x + 2
8x - 19y = 2 --- Eqn 1

x + y = 7 --- Eqn2

From Eqn 1 & 2,
-27y = -54
y = 2
x = 5

Number = 52

IMO-A

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The digit in the units place of a number is equal to the digit in the 02 Aug 2021, 10:31
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Bunuel
The digit in the units place of a number is equal to the digit in the tens place of half of that number and the digit in the tens place of that number is less than the digit in units place of half of the number by 1. If the sum of the digits of the number is seven, then what is the number?

(A) 52
(B) 34
(C) 16
(D) 15
(E) 14
D, E eliminated since summation is not 7.
Starting with option A,
Unit digit is 2, the tens digit is 5
Half the number 52/2= 26
So, the unit digit and the tenth of half the digit (52) are the same (2).
And also, the tenth digit (5) number is less than the unit digit (6) by 1.
So, the answer is A.
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The digit in the units place of a number is equal to the digit in the 03 Aug 2021, 00:09
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Quote:
Bunuel
The digit in the units place of a number is equal to the digit in the tens place of half of that number and the digit in the tens place of that number is less than the digit in units place of half of the number by 1. If the sum of the digits of the number is seven, then what is the number?

(A) 52
(B) 34
(C) 16
(D) 15
(E) 14
D, E eliminated since summation is not 7.
Starting with option A,
Unit digit is 2, the tens digit is 5
Half the number 52/2= 26
So, the unit digit and the tenth of half the digit (52) are the same (2).
And also, the tenth digit (5) number is less than the unit digit (6) by 1.
So, the answer is A.


can you plz make equation for this?
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ShahadatHJ
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The digit in the units place of a number is equal to the digit in the 03 Aug 2021, 08:59
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jrk23
Quote:
Bunuel
The digit in the units place of a number is equal to the digit in the tens place of half of that number and the digit in the tens place of that number is less than the digit in units place of half of the number by 1. If the sum of the digits of the number is seven, then what is the number?

(A) 52
(B) 34
(C) 16
(D) 15
(E) 14
D, E eliminated since summation is not 7.
Starting with option A,
Unit digit is 2, the tens digit is 5
Half the number 52/2= 26
So, the unit digit and the tenth of half the digit (52) are the same (2).
And also, the tenth digit (5) number is less than the unit digit (6) by 1.
So, the answer is A.


can you plz make equation for this?
Dear jrk23, please see the equation-based solution provided by rajatchopra1994. I think if I could, I would go with his equations.
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The digit in the units place of a number is equal to the digit in the 04 Aug 2021, 18:32
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ShahadatHJ
The digit in the units place of a number is equal to the digit in the tens place of half of that number and the digit in the tens place of that number is less than the digit in units place of half of the number by 1. If the sum of the digits of the number is seven, then what is the number?

(A) 52
(B) 34
(C) 16
(D) 15
(E) 14
D, E eliminated since summation is not 7.
Starting with option A,
Unit digit is 2, the tens digit is 5
Half the number 52/2= 26
So, the unit digit and the tenth of half the digit (52) are the same (2).
And also, the tenth digit (5) number is less than the unit digit (6) by 1.
So, the answer is A.[/quote]


can you plz make equation for this?[/quote]
Dear jrk23, please see the equation-based solution provided by rajatchopra1994. I think if I could, I would go with his equations.[/quote]

i am not able to get how he made first equation. can you plz elaborate.

Thanku :)
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ShahadatHJ
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The digit in the units place of a number is equal to the digit in the 05 Aug 2021, 06:24
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jrk23
ShahadatHJ
The digit in the units place of a number is equal to the digit in the tens place of half of that number and the digit in the tens place of that number is less than the digit in units place of half of the number by 1. If the sum of the digits of the number is seven, then what is the number?

(A) 52
(B) 34
(C) 16
(D) 15
(E) 14
D, E eliminated since summation is not 7.
Starting with option A,
Unit digit is 2, the tens digit is 5
Half the number 52/2= 26
So, the unit digit and the tenth of half the digit (52) are the same (2).
And also, the tenth digit (5) number is less than the unit digit (6) by 1.
So, the answer is A.


can you plz make equation for this?[/quote]
Dear jrk23, please see the equation-based solution provided by rajatchopra1994. I think if I could, I would go with his equations.[/quote]

i am not able to get how he made first equation. can you plz elaborate.

Thanku :)[/quote]
Suppose,
The digit in unit place is Y
The digit in tenth place is 10X
Then the original number is 10X+Y
Half the original number is (10X+Y)/2
So, according to the question, If you half the original number, (10X+Y)/2, then the tenth digit in the result is equal to the unit digit of the original number. So, after getting half the number we get 10Y in the tenth's place (unit digit becomes tenth digit). And also, the tenth digit in the original number, 10X, is less than the unit digit of half the original number is less than 1, when halved. Since X becomes the unit digit number and it is short by 1, we add 1 to the unit digit number X, and the unit digit becomes (X+1).
Now we can construct the equation as following one,
\((10X+Y)/2\)=10Y+(X+1)
And you develop the equation.

I hope you will get it. This question is really a good one because of the wording. However, I prefer my way of solving this question.
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The digit in the units place of a number is equal to the digit in the 24 Oct 2024, 07:59
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