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If x is a two-digit integer and the ratio of its units digit to its te

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Bunuel
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If x is a two-digit integer and the ratio of its units digit to its te [#permalink] If x is a two-digit integer and the ratio of its units digit to its te   19 Jun 2018, 02:19
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If x is a two-digit integer and the ratio of its units digit to its tens digit is 2 to 1, what is the value of x ?

(1) The units digit of x is 4 more than its tens digit.
(2) The product of the two-digits in x is 32.
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If x is a two-digit integer and the ratio of its units digit to its te [#permalink] If x is a two-digit integer and the ratio of its units digit to its te   19 Jun 2018, 02:30
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Let the unit digit be B and the ten's digit be A.
Thus X will be :

X =10A+B ....... (i)

Now we have been giveb that : B/A = 2/1
: B = 2A
Putting this in the equation (i) we get : X =12A .

Now considering option (1) :

B = A+4 .... (ii) putting value of B from (i) we get :
2A=A+4
A=4.
Thus X = 48. {sufficient}

Considering option (ii) :

AB = 32;
B=2A ; 2A^2 = 32 ; A = 4;

thus X = 10*4+2*4 = 48.

This is also sufficient.

Thus both options are individually sufficient to answer the question.
Answer : D

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Re: If x is a two-digit integer and the ratio of its units digit to its te [#permalink] If x is a two-digit integer and the ratio of its units digit to its te   19 Jun 2018, 02:46
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Bunuel wrote:
If x is a two-digit integer and the ratio of its units digit to its tens digit is 2 to 1, what is the value of x ?

(1) The units digit of x is 4 more than its tens digit.
(2) The product of the two-digits in x is 32.


Now, from the question, it is clear that unit digit of x is twice of its tens digit since x is a two-digit integer.
Therefore, x can have following 4 values
12,
24,
36, and
48.

Now from statement 1 :- x = 48, Hence Sufficient
From statement 2 - x= 48, Hence Sufficient

Thus, Ans = D
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Re: If x is a two-digit integer and the ratio of its units digit to its te [#permalink] If x is a two-digit integer and the ratio of its units digit to its te   20 Jun 2018, 11:45
x is ab
b = 2a

(1) b = a + 4
a = 4; 48

(1) ab = 32
2a^2 = 32
a = 4, -4; 48
since can't have two negative digits

Answer D. Each statement alone is sufficient
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Re: If x is a two-digit integer and the ratio of its units digit to its te [#permalink]
20 Jun 2018, 11:45
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Bunuel
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