The digit in the units place of a number is equal to the digit in the

Question

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

(A) 52 
(B) 34
(C) 16
(D) 15 
(E) 14

rajatchopra1994 · Answer

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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ShahadatHJ · Answer

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.

ShahadatHJ · Answer

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.

ArmaanBajaj · Answer

couldn't understand the question

Bunuel · Answer

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

(A) 52 
 (B) 34 
 (C) 16 
 (D) 15 
 (E) 14

Let the number be 10x + y, where x is the tens digit and y is the units digit.

The digit in the units place of the number is equal to the digit in the tens place of half of that number. 
 This means the tens digit of (10x + y)/2 is y.

The digit in the tens place of the number is less than the digit in the units place of half of the number by 1. 
 This means the units digit of (10x + y)/2 is x + 1.

The sum of the digits is 7. 
 So x + y = 7.

Test each option.

For 52, half the number is 26. The tens digit of 26 is 2, which equals y, and the units digit of 26 is 6, which is one more than x = 5. The sum of digits 5 + 2 = 7. All conditions are satisfied.

No other option fits.

Answer: A.

Arungmat612 · Answer

Bunuel  couldnot understand how you translated the given info into equations

Bunuel · Answer

Rewrite each sentence exactly as it says about digits.

The number is 10x + y, where x is the tens digit and y is the units digit.

Units digit of the number is y.
Tens digit of half the number is also y.
That is why we write: tens digit of (10x + y)/2 is y.

Tens digit of the number is x.
Units digit of half the number must be x + 1.
That is why we write: units digit of (10x + y)/2 is x + 1.

Done.

Arungmat612 · Answer

Bunuel  thanks for the detailed explanation. But still its tough for me to wrap my head across these kind of word problems. Is there any other similar questions from which i can practice?

RonPurewal · Answer

I don't recall ever seeing an official problem containing this much verbiage about digits. In my experience, GMAC tends to do one of two things: /1/ use a phrase like "units digit" or "tens digit" if only one or maybe two digits appear in the problem statement, or else /2/ represent the situation in more traditional mathematical or algebraic notation using uppercase letters for the digits, if multiple digits are involved. Here's an example of an official problem of the latter kind, with uppercase (capital) letters representing digits: https://gmatclub.com/forum/in-the-corre ... 21720.html (GMAC will not use lowercase letters to represent digits.) If GMAC serves you a problem like the one in this thread, the digits in that problem will almost certainly be represented by uppercase letters (since four different digits figure into the problem statement). In that case, the problem statement in this thread would read as follows: A two-digit number AB is twice another two-digit number CD, where the letters A, B, C, D represent digits. If B = C, A = D – 1, and A + B = 7, then the number AB is:

The digit in the units place of a number is equal to the digit in the

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The digit in the units place of a number is equal to the digit in the

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