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16 Mar 2020, 01:52
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Let an infinite sequence of positive integers be termed "pure" if it contains no numbers divisible by 3 or by 7. Is infinite sequence M "pure"?
(1) M contains only prime numbers.
(2) The units digit of all members of M is either 3 or 7.
Let an infinite series of positive integers be termed "pure" if it contains no numbers divisible by 3 or by 7. Is infinite series M "pure"?
1) M contains only prime numbers.
2) The ones digit of all members of M is either 3 or 7.
1) M contains only prime numbers.
2) The ones digit of all members of M is either 3 or 7.
Updated on: 17 Mar 2020, 12:30
Originally posted by freedom128 on 16 Mar 2020, 03:48.
Last edited by freedom128 on 17 Mar 2020, 12:30, edited 2 times in total.
Last edited by freedom128 on 17 Mar 2020, 12:30, edited 2 times in total.
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(1) M contains only prime numbers = 2,3,5,7,...
If M ={2,5,11,13,17,...}, then M is pure
If M ={3,7,13,17,...}, then M is not pure
NOT SUFFICIENT
(2) The units digit of all members of M is either 3 or 7.
If M ={13,17,23,37,...}, then M is pure
If M ={3,7,13,17,23,37...}, then M is not pure
NOT SUFFICIENT
(1)+(2)
If M ={13,17,23,37,...}, then M is pure
If M ={3,7,13,17,...}, then M is not pure
NOT SUFFICIENT
FINAL ANSWER IS (E)
If M ={2,5,11,13,17,...}, then M is pure
If M ={3,7,13,17,...}, then M is not pure
NOT SUFFICIENT
(2) The units digit of all members of M is either 3 or 7.
If M ={13,17,23,37,...}, then M is pure
If M ={3,7,13,17,23,37...}, then M is not pure
NOT SUFFICIENT
(1)+(2)
If M ={13,17,23,37,...}, then M is pure
If M ={3,7,13,17,...}, then M is not pure
NOT SUFFICIENT
FINAL ANSWER IS (E)
Updated on: 17 Mar 2020, 03:18
Originally posted by CareerGeek on 16 Mar 2020, 03:48.
Last edited by CareerGeek on 17 Mar 2020, 03:18, edited 1 time in total.
Last edited by CareerGeek on 17 Mar 2020, 03:18, edited 1 time in total.
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(1) M contains only prime numbers.
Case 1: Possible values of M = {2, 3, 5, 7, . . . . . } --> Not Pure
Case 2: Possible values of M = {2, 5, . . . . . } --> Pure
--> Insufficient
(2) The units digit of all members of M is either 3 or 7.
Case 1: Possible values of M = {3, 7, 13, 17, 23, 27, 33, . . . . . . . } --> Not Pure
Case 2: Possible values of M = {13, 17, 27, 37, . . . . . . . } --> Pure
--> Insufficient
Combining (1) & (2),
Case 1: M ={13, 17, 23, 37,...} --> Pure
Case 2: M ={3, 7, 13, 17,...} --> Not Pure
--> Insufficient
Option E
Case 1: Possible values of M = {2, 3, 5, 7, . . . . . } --> Not Pure
Case 2: Possible values of M = {2, 5, . . . . . } --> Pure
--> Insufficient
(2) The units digit of all members of M is either 3 or 7.
Case 1: Possible values of M = {3, 7, 13, 17, 23, 27, 33, . . . . . . . } --> Not Pure
Case 2: Possible values of M = {13, 17, 27, 37, . . . . . . . } --> Pure
--> Insufficient
Combining (1) & (2),
Case 1: M ={13, 17, 23, 37,...} --> Pure
Case 2: M ={3, 7, 13, 17,...} --> Not Pure
--> Insufficient
Option E
