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Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8009
GMAT 1: 760 Q51 V42 GPA: 3.82
If n is a 2-digit positive integer and its tens digit is 4 times its u  [#permalink]

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Difficulty:   25% (medium)

Question Stats: 79% (01:14) correct 21% (01:24) wrong based on 71 sessions

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[Math Revolution GMAT math practice question]

If n is a 2-digit positive integer and its tens digit is 4 times its units digit, what is the value of n?

1) The tens digit of n is 8.
2) The sum of the tens digit and the units digit of n is 2-digit integer.

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If n is a 2-digit positive integer and its tens digit is 4 times its u  [#permalink]

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MathRevolution wrote:
[Math Revolution GMAT math practice question]

If n is a 2-digit positive integer and its tens digit is 4 times its units digit, what is the value of n?

1) The tens digit of n is 8.
2) The sum of the tens digit and the units digit of n is 2-digit integer.

St1:- The tens digit of n is 8.
Given, tens digit is 4 times its units digit.
So, units digit is $$\frac{8}{4}=2$$
Therefore, the 2-digit positive integer, n is 82.
Sufficient.

St2:-The sum of the tens digit and the units digit of n is 2-digit integer.
If units digit is y and tens digit is x, then n=10x+y.
n=x y or 4y y

Since, x+y is a 2-digit integer, we have y=2 as unit digit. So, tens digit=4y=4*2=8.
So, n=10x+y=10*8+2=82

Sufficient.

Ans. (D)
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Re: If n is a 2-digit positive integer and its tens digit is 4 times its u  [#permalink]

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(1) Tens digit= 8.

So Unit digit is $$\frac{8}{4}$$= 2

Value of n=82 [Suff]

(2) Only 82 fulfill the condition given in statement 2.

Value of n=82 [Suff]

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If n is a 2-digit positive integer and its tens digit is 4 times its u  [#permalink]

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PKN wrote:
MathRevolution wrote:
[Math Revolution GMAT math practice question]

If n is a 2-digit positive integer and its tens digit is 4 times its units digit, what is the value of n?

1) The tens digit of n is 8.
2) The sum of the tens digit and the units digit of n is 2-digit integer.

St1:- The tens digit of n is 8.
Given, tens digit is 4 times its units digit.
So, units digit is $$\frac{8}{4}=2$$
Therefore, the 2-digit positive integer, n is 82.
Sufficient.

St2:-The sum of the tens digit and the units digit of n is 2-digit integer.
If units digit is y and tens digit is x, then n=10x+y.
n=x y or 4y y

Since, x+y is a 2-digit integer, we have y=2 as unit digit. So, tens digit=4y=4*2=8.
So, n=10x+y=10*8+2=82

Sufficient.

Ans. (D)

Hi PKN

can you please elaborate on statement TWO

St2:-The sum of the tens digit and the units digit of n is 2-digit integer.
If units digit is y and tens digit is x, then n=10x+y.
n=x y or 4y y

Since, x+y is a 2-digit integer, we have y=2 as unit digit. So, tens digit=4y=4*2=8.
So, n=10x+y=10*8+2=82

are you using remainder formula ? n=10x+y. X is quotient and Y is remainer ? why ? any other method to explain second statement? you explanation is kinda hard to understand thanks problem solver killer i think your username could be PSK instead of PKN Director  G
Joined: 20 Feb 2015
Posts: 764
Concentration: Strategy, General Management
Re: If n is a 2-digit positive integer and its tens digit is 4 times its u  [#permalink]

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1
MathRevolution wrote:
[Math Revolution GMAT math practice question]

If n is a 2-digit positive integer and its tens digit is 4 times its units digit, what is the value of n?

1) The tens digit of n is 8.
2) The sum of the tens digit and the units digit of n is 2-digit integer.

A two digit number = ab
can also be written as 10a+b (21 =10*2+1)

also ,

a=4b ( as given in the question)

1) The tens digit of n is 8.

given a = 8
substituting the value b=2
n=82
suficient

2) The sum of the tens digit and the units digit of n is 2-digit integer.
a+b= cd a 2 digit number
we are already given
a=4b
the minimum value a can take is 4 when b= 1
but 4+1=5 doesnot satisfy the condition
it will satisfy the condition only when b=2 and a=8
so, 8+2= a two digit number

D it should be !!

realized no need for 10a + b stuff !!
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Posts: 764
Concentration: Strategy, General Management
If n is a 2-digit positive integer and its tens digit is 4 times its u  [#permalink]

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dave13 wrote:
PKN wrote:
MathRevolution wrote:
[Math Revolution GMAT math practice question]

If n is a 2-digit positive integer and its tens digit is 4 times its units digit, what is the value of n?

1) The tens digit of n is 8.
2) The sum of the tens digit and the units digit of n is 2-digit integer.

St1:- The tens digit of n is 8.
Given, tens digit is 4 times its units digit.
So, units digit is $$\frac{8}{4}=2$$
Therefore, the 2-digit positive integer, n is 82.
Sufficient.

St2:-The sum of the tens digit and the units digit of n is 2-digit integer.
If units digit is y and tens digit is x, then n=10x+y.
n=x y or 4y y

Since, x+y is a 2-digit integer, we have y=2 as unit digit. So, tens digit=4y=4*2=8.
So, n=10x+y=10*8+2=82

Sufficient.

Ans. (D)

Hi PKN

can you please elaborate on statement TWO

St2:-The sum of the tens digit and the units digit of n is 2-digit integer.
If units digit is y and tens digit is x, then n=10x+y.
n=x y or 4y y

Since, x+y is a 2-digit integer, we have y=2 as unit digit. So, tens digit=4y=4*2=8.
So, n=10x+y=10*8+2=82

are you using remainder formula ? n=10x+y. X is quotient and Y is remainer ? why ? any other method to explain second statement? you explanation is kinda hard to understand thanks problem solver killer i think your username could be PSK instead of PKN what he probably meant was n= 10x+y
from question stem x=4y
so n= 40y+y
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Re: If n is a 2-digit positive integer and its tens digit is 4 times its u  [#permalink]

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dave13 wrote:
PKN wrote:
MathRevolution wrote:
[Math Revolution GMAT math practice question]

If n is a 2-digit positive integer and its tens digit is 4 times its units digit, what is the value of n?

1) The tens digit of n is 8.
2) The sum of the tens digit and the units digit of n is 2-digit integer.

St1:- The tens digit of n is 8.
Given, tens digit is 4 times its units digit.
So, units digit is $$\frac{8}{4}=2$$
Therefore, the 2-digit positive integer, n is 82.
Sufficient.

St2:-The sum of the tens digit and the units digit of n is 2-digit integer.
If units digit is y and tens digit is x, then n=10x+y.
n=x y or 4y y

Since, x+y is a 2-digit integer, we have y=2 as unit digit. So, tens digit=4y=4*2=8.
So, n=10x+y=10*8+2=82

Sufficient.

Ans. (D)

Hi PKN

can you please elaborate on statement TWO

St2:-The sum of the tens digit and the units digit of n is 2-digit integer.
If units digit is y and tens digit is x, then n=10x+y.
n=x y or 4y y

Since, x+y is a 2-digit integer, we have y=2 as unit digit. So, tens digit=4y=4*2=8.
So, n=10x+y=10*8+2=82

are you using remainder formula ? n=10x+y. X is quotient and Y is remainder ? why ? any other method to explain second statement? you explanation is kinda hard to understand thanks problem solver killer i think your username could be PSK instead of PKN Hi dave13,

You know ,we can express any number in the following form:-

1. 3-digit number, XYZ=100X+10Y+Z
Example, 123=100*1+10*2+3=100+20+3=123

2. 2-digit number, XY=10X+Y
Example, 12=10*1+2=10+2=12

In my explanation, I have considered XY, the 2-digit positive integer, where X and Y are the tens and units digit respectively.
So, as per above algebra form of a 2-digit number, we can write n=10*X+Y.----------(1)
Hope you agree.
Refer question , it is told that "tens digit is 4 times its units digit." So, X=4*Y--------------(2)
In st2, we are told that "the sum of the tens digit and the units digit of n is 2-digit integer.
Now, kindly refer the enclosure for furtherance.

Hope it helps.
Attachments 2-digit.JPG [ 67.2 KiB | Viewed 676 times ]

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PKN

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Re: If n is a 2-digit positive integer and its tens digit is 4 times its u  [#permalink]

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many thanks friends PKN and CounterSniper for wonderful explanations Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8009
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: If n is a 2-digit positive integer and its tens digit is 4 times its u  [#permalink]

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=>

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question.

$$n = 10a + b$$ and $$a = 4b$$
The possible pairs $$( a, b )$$ are $$( 4, 1 )$$ and $$( 8, 2 )$$ by the original condition.
Thus, $$n = 41$$ or $$n = 82$$.

Since we have $$3$$ variables and $$2$$ equations, D is most likely to be the answer. So, we should consider each of the conditions on its own first.

Condition 1)
Since $$a = 8$$, we must have $$n = 82$$.
Thus, condition 1) is sufficient.

Condition 2)
Since $$4 + 1 = 5$$ is not a 2-digit integer and $$8 + 2 = 10$$ is a 2-digit integer, $$n = 82.$$
Thus, condition 2) is sufficient.

Therefore, D is the answer.

If the original condition includes “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations” etc., one more equation is required to answer the question. If each of conditions 1) and 2) provide an additional equation, there is a 59% chance that D is the answer, a 38% chance that A or B is the answer, and a 3% chance that the answer is C or E. Thus, answer D (conditions 1) and 2), when applied separately, are sufficient to answer the question) is most likely, but there may be cases where the answer is A,B,C or E.
_________________ Re: If n is a 2-digit positive integer and its tens digit is 4 times its u   [#permalink] 09 Aug 2018, 01:29
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