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N is a 3digit number, and the sum o [#permalink]
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11 Jun 2018, 07:01
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54% (01:33) correct 46% (01:51) wrong based on 50 sessions
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N is a 3digit number, and the sum of its digits is 10. When the digits of N are reversed, the new number is 99 less than N. What is the value of N? (1) The hundreds digit of N is 1 more than its units digit. (2) The tens digit of N is 2 more than its hundreds digit. *kudos for all correct solutions
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Re: N is a 3digit number, and the sum o [#permalink]
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11 Jun 2018, 07:34
Solution Given:• N is a 3digit number • Sum of the digits of N is 10 • When N is reversed, the new number is 99 less than N To find:Approach and Working: If we assume N = abc, then reverse of N = cba As N – reverse of N = 99, we can write, • abc – cba = 99 Or, 100a + 10b + c – 100c – 10b – a = 99 Or, 99 (a – c) = 99 Or, a – c = 1 As both a and c are singledigit integers, the possible values of (a, c) = (2, 1), (3, 2), (4, 3), (5, 4) [(6, 5) onwards values are not possible as sum of the digits is equal to 10] Using the relation, a + b + c = 10, the possible value sets of (a, b, c) = (2, 7, 1), (3, 5, 2), (4, 3, 3), (5, 1, 4) Analysing Statement 1• As per the information given in statement 1, a = 1 + c
o This is an information that we have already derived, and not giving us any new information Hence, statement 1 is not sufficient to answer Analysing Statement 2• As per the information given in statement 2, b = 2 + a • From the possible values of (a, b, c) we can have only one case where it is getting satisfied = (3, 5, 2) Therefore, the number N = 352 Hence, statement 2 is sufficient to answer Hence, the correct answer is option B. Answer: B
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Re: N is a 3digit number, and the sum o [#permalink]
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11 Jun 2018, 07:35
GMATPrepNow wrote: N is a 3digit number, and the sum of its digits is 10. When the digits of N are reversed, the new number is 99 less than N. What is the value of N?
(1) The hundreds digit of N is 1 more than its units digit. (2) The tens digit of N is 2 more than its hundreds digit.
*kudos for all correct solutions Let's represent N as abc where: a = hundreds digit b = tens digit c = ones digit Therefore algebraically: N = 100a + 10b + c Reverse N = 100c + 10b + a Given: N = Reverse N + 99 > 100a + 10b + c = 100c + 10b + a + 99 Simplify: 99a = 99c + 99 > a = c + 1 From given info we know: a = c + 1 a + b + c = 10 Our goal is to solve for N by finding a,b and c Statement 1 Tells us a = c + 1. We already know this info so its not helpful > INSUFFICIENT Statement 2 says b = a + 2 Therefore everything can be written in terms of a: a = a b = a + 2 c = a  1 Since a + b + c = 10 > a + (a+2) + (a  1) = 10 > a = 3 > c = 2 > b = 5 Therefore N is 352. > sufficient Answer: B Sent from my SMG920T using GMAT Club Forum mobile app
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N is a 3digit number, and the sum o [#permalink]
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11 Jun 2018, 09:25
GMATPrepNow wrote: N is a 3digit number, and the sum of its digits is 10. When the digits of N are reversed, the new number is 99 less than N. What is the value of N?
(1) The hundreds digit of N is 1 more than its units digit. (2) The tens digit of N is 2 more than its hundreds digit.
*kudos for all correct solutions Since we get a 3digit number(reversed) after subtracting 99 from N(3digit integer), therefore N must be greater than 200. Property: When the digits of a 3digit number are reversed after subtracting the original number by 99, the hundred's place digit is one more than the unit's place digit.Question stem: N=? Statement1: As mentioned above in the property, this statement doesn't provide additional info. So, st1 is insufficient. Statement2 The affixed table may be referred. From the table, N=352. Hence, statement2 is sufficient. Ans. B Hope my logic is correct.
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N is a 3digit number, and the sum o [#permalink]
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11 Jun 2018, 14:24
GMATPrepNow wrote: N is a 3digit number, and the sum of its digits is 10. When the digits of N are reversed, the new number is 99 less than N. What is the value of N?
(1) The hundreds digit of N is 1 more than its units digit. (2) The tens digit of N is 2 more than its hundreds digit.
*kudos for all correct solutions We are given the following information in the question stem: 1. Let N(3 digit number) be xyz where x  hundred's digit, y  ten's digit, z  one's digit. 2. x+y+z = 10. 3. xyz  zyx = 99(Here zyx is the reverse of the number N) We have been asked the value of N. 1. When the hundred's digit of N is 1 more than it's units digit, there are 4 possibilities: 271,352,433,514. Reversing these 4 numbers we will get 172,253,334,415 & each of these 4 numbers when subtracted from the number it reverses, gives us 99. We can't find a unique value for N. (Insufficient)2. If the tens digit of N is 2 more than its hundreds digit, there are 3 possibilities: 136,244,352. Reversing these 3 numbers, we will get 631,442,253. Only 352  253 gives 99, making 352 our number (Sufficient  Option B)
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Re: N is a 3digit number, and the sum o [#permalink]
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13 Jun 2018, 08:29
GMATPrepNow wrote: N is a 3digit number, and the sum of its digits is 10. When the digits of N are reversed, the new number is 99 less than N. What is the value of N?
(1) The hundreds digit of N is 1 more than its units digit. (2) The tens digit of N is 2 more than its hundreds digit.
*kudos for all correct solutions Target question: What is the value of N? Given: N is a 3digit number, and the sum of its digits is 10. When the digits of N are reversed, the new number is 99 less than N. Let N = wxy, where w, x and y represent the 3 digits in N So, the first equation we can write is: w + x + y = 10Now let's examine the situation where we REVERSE the digits. First of all, the VALUE of N (wxy) is equal to 100w + 10x + y Next, the VALUE of the REVERSED number (yxw) is equal to 100y + 10x + w Since the REVERSED number is 99 less than N, we can write: 100y + 10x + w = 100w + 10x + y  99 Subtract w from both sides: 100y + 10x = 99w + 10x + y  99 Subtract 10x from both sides: 100y = 99w + y  99 Subtract y from both sides: 99y = 99w  99 Divide both sides by 99 to get: y = w  1Now onto the statements.... Statement 1: The hundreds digit of N is 1 more than its units digit. In other words, w = y + 1, which is the SAME as y = w  1Notice that this provides NO NEW INFORMATION, since we already concluded that y = w  1Since statement 1 provides no new information, it is NOT SUFFICIENT Statement 2: The tens digit of N is 2 more than its hundreds digit. In other words, x = w + 2Now that we've written x and w in terms of w (i.e., x = w + 2 and y = w  1), we can take the given information ( w + x + y = 10), and replace w and x When we do so, we get: w + ( w + 2) + ( w  1) = 10 Simplify: 3w + 1 = 10 Solve: w = 3 If w = 3, then x = 5, and y = 2 So, N =352Since we can answer the target question with certainty, statement 2 is SUFFICIENT Answer: B Cheers, Brent
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