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If n is a 2-digit positive integer and its tens digit is 4 times its u

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
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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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07 Aug 2018, 00:59
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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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"Only $79 for 1 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" VP Status: Learning stage Joined: 01 Oct 2017 Posts: 1014 WE: Supply Chain Management (Energy and Utilities) If n is a 2-digit positive integer and its tens digit is 4 times its u [#permalink] Show Tags 07 Aug 2018, 01:12 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. 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) _________________ Regards, PKN Rise above the storm, you will find the sunshine Senior Manager Joined: 07 Jul 2012 Posts: 367 Location: India Concentration: Finance, Accounting GPA: 3.5 Re: If n is a 2-digit positive integer and its tens digit is 4 times its u [#permalink] Show Tags 07 Aug 2018, 02:45 (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] Answer: D. _________________ Kindly hit kudos if my post helps! VP Joined: 09 Mar 2016 Posts: 1230 If n is a 2-digit positive integer and its tens digit is 4 times its u [#permalink] Show Tags 07 Aug 2018, 07:37 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 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] Show Tags 07 Aug 2018, 08:11 1 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 !! Director Joined: 20 Feb 2015 Posts: 764 Concentration: Strategy, General Management If n is a 2-digit positive integer and its tens digit is 4 times its u [#permalink] Show Tags 07 Aug 2018, 08:18 1 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 VP Status: Learning stage Joined: 01 Oct 2017 Posts: 1014 WE: Supply Chain Management (Energy and Utilities) Re: If n is a 2-digit positive integer and its tens digit is 4 times its u [#permalink] Show Tags 07 Aug 2018, 08:58 1 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 ] _________________ Regards, PKN Rise above the storm, you will find the sunshine VP Joined: 09 Mar 2016 Posts: 1230 Re: If n is a 2-digit positive integer and its tens digit is 4 times its u [#permalink] Show Tags 07 Aug 2018, 10:00 1 many thanks friends PKN and CounterSniper for wonderful explanations Math Revolution GMAT Instructor 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] Show Tags 09 Aug 2018, 01:29 => 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. Answer: D 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. _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$79 for 1 month Online Course"
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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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