A positive 5-digit integer is called "friendly" if

Question

GMATH practice exercise (Quant Class 18) A positive 5-digit integer is called "friendly" if each of its digits is 1,2,3,4 or 5 and all of its digits are different. Putting all friendly numbers in increasing order, the units digit of the friendly number that occupies the 32nd place is: (A) 5 (B) 4 (C) 3 (D) 2 (E) 1 Answer: [spoiler]____(B)__[/spoiler]

GMATGuruNY · Answer

fskilnik@GMATH wrote:GMATH practice exercise (Quant Class 18) A positive 5-digit integer is called "friendly" if each of its digits is 1,2,3,4 or 5 and all of its digits are different. Putting all friendly numbers in increasing order, the units digit of the friendly number that occupies the 32nd place is: (A) 5 (B) 4 (C) 3 (D) 2 (E) 1 Total number of friendly numbers = total number of ways to arrange the 5 digits = 5! = 120. There are 5 options for the first digit: 1, 2, 3, 4, or 5. 120/5 = 24. Thus, the 120 friendly numbers are composed of five 24-number ranges, as follows: The integers beginning with 1 constitute friendly numbers 1-24. The integers beginning with 2 constitute friendly numbers 25-48. The integers beginning with 3 constitute friendly numbers 49-72. The integers beginning with 4 constitute friendly numbers 73-96. The integers beginning with 5 constitute friendly numbers 97-120. The 32nd friendly number is contained within the blue range above. Friendly numbers in the blue range, from least to greatest: 21345 --> 25th friendly number 21354 --> 26th friendly number 21435 --> 27th friendly number 21453 --> 28th friendly number 21534 --> 29th friendly number 21543 --> 30th friendly number 23145 --> 31st friendly number 23154 --> 32nd friendly number The units digit for the 32nd friendly number = 4. The correct answer is B.

fskilnik@GMATH · Answer

fskilnik@GMATH wrote:GMATH practice exercise (Quant Class 18) A positive 5-digit integer is called "friendly" if each of its digits is 1,2,3,4 or 5 and all of its digits are different. Putting all friendly numbers in increasing order, the units digit of the friendly number that occupies the 32nd place is: (A) 5 (B) 4 (C) 3 (D) 2 (E) 1 FOCUS: the units digit of the 32nd friendly number 1. The first P4 = 4! = 24 friendly numbers "start with 1" (i.e., 1 _ _ _ _ ) , the (few) next ones "start with 2". 2. "Starting with 2" (i.e., 2 _ _ _ _ ), there are P3 = 3! = 6 friendly numbers "beginning with 21" (i.e., 2 1 _ _ _ ), hence: All friendly numbers, from the 25th until the 30th (both included) are of the form 21 _ _ _ . 3. The 31st friendly number is the smallest friendly number that starts with "23", that is, 23145. 4. Finally, the 32nd friendly number is the next one (23154), hence ? = 4. The correct answer is (B). We follow the notations and rationale taught in the GMATH method. Regards, Fabio.

Choose how you want to prepare

Get Ready for GMAT Test Day Faster with Live Online Classes

Target Test Prep EA OnDemand

Target Test Prep GMAT OnDemand

A positive 5-digit integer is called "friendly" if

Chicago Booth

GMAT Course Reviews

Admissions Consulting Reviews

FREE GMAT PREP RESOURCES

GMAT PREP DEAL TRACKER