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100 points for $49 worth of Veritas practice GMATs FREE VERITAS PRACTICE GMAT EXAMS Earn 10 Points Per Post Earn 10 Points Per Thanks Earn 10 Points Per Upvote Is the three-digit number n less than 550? This topic has 2 expert replies and 0 member replies Top Member Is the three-digit number n less than 550? Timer 00:00 Your Answer A B C D E Global Stats Difficult Is the three-digit number n less than 550? (1) The product of the digits in n is 30. (2) The sum of the digits in n is 10. OA C Source: GMAT Prep GMAT/MBA Expert GMAT Instructor Joined 22 Aug 2016 Posted: 1890 messages Followed by: 30 members Upvotes: 470 Top Reply BTGmoderatorDC wrote: Is the three-digit number n less than 550? (1) The product of the digits in n is 30. (2) The sum of the digits in n is 10. OA C Source: GMAT Prep Given: n is a three-digit number. Question: Is n < 550? Let's take each statement one by one. (1) The product of the digits in n is 30. 30 = 1*2*3*5 Case 1: Say n = 615. The answer is no. Case 2: Say n = 156. The answer is yes. No unique answer. Insufficient. (2) The sum of the digits in n is 10. Case 1: Say n = 910. The answer is no. Case 2: Say n = 190. The answer is yes. No unique answer. Insufficient. (1) and (2) together Given the product of the digits = 30 = 1*2*3*5, we must have one of the digits equal to 5, and given that the sum of the digits equals to 10, the sum of other two digits equals to 10 - 5 = 5; thus, the other two digits must be 2 and 3. With three digits 2, 3, and 5, we can have a maximum number = 532, which is less than 550. The answer is yes. Sufficient. The correct answer: C Hope this helps! -Jay _________________ Manhattan Review GMAT Prep Locations: Manhattan Review India | Manhattan Review Hyderabad | Madhapur GMAT Courses | Dilsukhnagar GRE Prep | and many more... Schedule your free consultation with an experienced GMAT Prep Advisor! Click here. GMAT/MBA Expert GMAT Instructor Joined 09 Oct 2010 Posted: 1449 messages Followed by: 32 members Upvotes: 59 Top Reply BTGmoderatorDC wrote: Is the (positive) three-digit number n less than 550? (1) The product of the digits in n is 30. (2) The sum of the digits in n is 10. Source: GMAT Prep Very nice problem! $100 \leqslant \,\,n = \left\langle {ABC} \right\rangle \,\, \leqslant 999$ $\left\langle {ABC} \right\rangle \,\,\mathop < \limits^? \,\,550$ $\left( 1 \right)\,\,\,A \cdot B \cdot C = 30\,\,\,\left\{ \begin{gathered} \,{\text{Take}}\,\,\left( {A,B,C} \right) = \left( {1,5,6} \right)\,\,\,\, \Rightarrow \,\,\,\,\left\langle {{\text{YES}}} \right\rangle \hfill \\ \,{\text{Take}}\,\,\left( {A,B,C} \right) = \left( {5,6,1} \right)\,\,\,\, \Rightarrow \,\,\,\,\left\langle {{\text{NO}}} \right\rangle \hfill \\ \end{gathered} \right.$ $\left( 2 \right)\,\,\,A + B + C = 10\,\,\,\left\{ \begin{gathered} \,{\text{Take}}\,\,\left( {A,B,C} \right) = \left( {1,2,7} \right)\,\,\,\, \Rightarrow \,\,\,\,\left\langle {{\text{YES}}} \right\rangle \hfill \\ \,{\text{Take}}\,\,\left( {A,B,C} \right) = \left( {5,5,0} \right)\,\,\,\, \Rightarrow \,\,\,\,\left\langle {{\text{NO}}} \right\rangle \hfill \\ \end{gathered} \right.$ $\left( {1 + 2} \right)\,\,\,\left\langle {ABC} \right\rangle \,\,\, \geqslant \,\,\,550\,\,\,\, \Rightarrow \,\,\,\left\{ \begin{gathered} \,A = 5\,\,,\,\,B \geqslant 5\,\,\,\mathop \Rightarrow \limits^{\left( 2 \right)} \,\,\,B = 5,\,\,C = 0\,\,\, \Rightarrow \,\,\,\left( 1 \right)\,\,{\text{contradicted}} \hfill \\ \,\,\,{\text{or}} \hfill \\ \,A \geqslant 6\,\,\,\mathop \Rightarrow \limits_{\left( 1 \right)}^{\left( * \right)} \,\,\,A = 6\,\,\,\mathop \Rightarrow \limits^{\left( 1 \right)} \,\,\,B \cdot C = 5\,\,\,\,\mathop \Rightarrow \limits^{\left( {**} \right)} \,\,\,A + B + C = 6 + 5 + 1\,\,\, \Rightarrow \,\,\,\left( 2 \right)\,\,{\text{contradicted}} \hfill \\ \end{gathered} \right.\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\left\langle {{\text{YES}}} \right\rangle$ $\left( * \right)\,\,\,\left( 1 \right)\,\,\, \Rightarrow \,\,\,A,B,C\,\,{\text{are}}\,\,\left( {{\text{positive}}} \right)\,\,{\text{divisors}}\,\,{\text{of}}\,\,30\,\,\, \Rightarrow \,\,\,A \notin \left\{ {7,8,9} \right\}$ $\left( {**} \right)\,\,\,B \cdot C = 5\,\,\, \Rightarrow \,\,\,B,C\,\,{\text{is}}\,\,{\text{a}}\,\,{\text{pair}}\,\,{\text{of}}\,\,\left( {{\text{positive}}} \right)\,\,{\text{divisors}}\,\,{\text{of}}\,\,5\,\,\, \Rightarrow \,\,\,\left\{ \begin{gathered} \,\left( {B,C} \right) = \left( {1,5} \right) \hfill \\ \,\,{\text{or}} \hfill \\ \,\left( {B,C} \right) = \left( {5,1} \right) \hfill \\ \end{gathered} \right.$ This solution follows the notations and rationale taught in the GMATH method. Regards, Fabio. _________________ Fabio Skilnik :: GMATH method creator ( Math for the GMAT) English-speakers :: https://www.gmath.net Portuguese-speakers :: https://www.gmath.com.br • Award-winning private GMAT tutoring Register now and save up to$200

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