Let an infinite series of positive integers be termed "pure" if it con

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Competition Mode Question

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.

freedom128 · Answer

(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)

CareerGeek · Answer

(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

Kinshook · Answer

Asked: 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.
Prime numbers include 3 & 7.
M = {3, 7, 11, 13, 17, ....} - Not "Pure"
M = {11, 13, 17, .... } - "Pure"
NOT SUFFICIENT

(2) The units digit of all members of M is either 3 or 7.
M = {3, 7, 11, 13, 17, ....} - Not "Pure"
M = {13, 17, 23.... } - "Pure"
NOT SUFFICIENT

(1) + (2) 
(1) M contains only prime numbers.
(2) The units digit of all members of M is either 3 or 7.
M = {3, 7, 11, 13, 17, ....} - Not "Pure"
M = {13, 17, 23.... } - "Pure"
NOT SUFFICIENT

IMO E

exc4libur · Answer

(1) insufic

not pure primes: {2,3,5,7…}
pure primes: {2,5,11…}

(2) insufic

not pure: {3,7,13,17…}
pure: {13,17,23…}

(1/2) insufic

not pure primes: {3,7,13,17…}
pure primes: {13,17,23…}

Ans (E)

Archit3110 · Answer

#1
M contains only prime numbers.
cannot be pure as 3,7 are prime and are divisible by 3 and 7 or may not be there as well; insufficient

#2
The units digit of all members of M is either 3 or 7.

again no ; can be 13,37 ; so the sequence is not Pure or can be pure if 27,63 are present 
insufficient
nothing in common 
IMO E

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.

unraveled · Answer

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"?

If no number divisible by 3 or 7 is present then sequence is pure
If a number divisible by either 3 or 7 is present then sequence is not pure

(1) M contains only prime numbers.
3 and 7 are present. Thus not pure.

SUFFICIENT.

(2) The units digit of all members of M is either 3 or 7.
Since its an infinite sequence it can contain
Case I: 3, 7 or 33, 27 - its not a pure sequence.
Case II: 13, 17, 23, 37, 43, 47 - its a pure sequence.

INSUFFICIENT.

Answer A.

chaitralirr · Answer

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.

Statement 1

If M contains only prime numbers it can contain 3 or 7 both are prime number hence statement 1 is insufficient.

Statement 2:

The units digit of all members of M is either 3 or 7

eg 23 Yes then M is pure
 if it has 3 or 7 only then M sequence is not pure.

Hence statement 2 is insufficient.

Combining 1 and 2 still insufficient as we don't know if 3 or 7 alone are part of the sequence.

IMO E

Let an infinite series of positive integers be termed "pure" if it con

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Let an infinite series of positive integers be termed "pure" if it con

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