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A sequence S consists of 5 distinct positive integers. Are all the int 13 May 2020, 06:58
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E
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60% (01:52) correct 40% (01:47) wrong based on 164 sessions

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A sequence S consists of 5 distinct positive integers. Are all the integers in the sequence divisible by 5?

(1) The sum of all the integers in the sequence is divisible by 5.
(2) The product of all the integers in the sequence is divisible by 5 but not by 10.

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E
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A sequence S consists of 5 distinct positive integers. Are all the int 13 May 2020, 07:05
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Bunuel
A sequence S consists of 5 distinct positive integers. Are all the integers in the sequence divisible by 5?

(1) The sum of all the integers in the sequence is divisible by 5.
(2) The product of all the integers in the sequence is divisible by 5 but not by 10.

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Question: Are all the integers in the sequence divisible by 5?

Statement 1: The sum of all the integers in the sequence is divisible by 5.

SUm is divisible does not ensure that all terma are divisible
e.g. {8, 9, 10, 11, 12} Sum is 50 i.e. divisible by 5 by each term is not divisible by 5
ALso, e.g. {5, 10, 15, 20, 25} Sum is 75 i.e. divisible by 5 by each term is divisible by 5
hence

NOT SUFFICIENT

Statement 2: The product of all the integers in the sequence is divisible by 5 but not by 10.

i.e. All the terms in series are ODD and atleast one of them must be divisible by 5
Set may be {5, 15, 25, 35, 45} YES OR {21, 23, 25, 27, 29} NO

NOT SUFFICIENT

COmbining the statements

Set may still be {5, 15, 25, 35, 45} YES OR {21, 23, 25, 27, 29} NO

NOT SUFFICIENT

ANswer: Option E
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A sequence S consists of 5 distinct positive integers. Are all the int 13 May 2020, 10:20
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St 1) Sum of all int is div by 5. Go small with testing number
1+2+3+4+5 is div by 5 but not all no are div by 5
5+10+15+20+25 is div by 5 and all no are div by 5
no
not suffi

St 2)Product of all no div by 5 and not 10
1*3*5*7*9 div by 5 (choose only one no div by 5 to make this suffi and make sure there is no even no so that it does not get div by 10)

5*15*25*35*45

Not suffi

Together
1*3*5*7*9 & 1+3+5+7+9=25; not all no divisible by 5
5*15*25*35*45 & 5+15+25+35+45 = 125; all no div by 5

(E)
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A sequence S consists of 5 distinct positive integers. Are all the int 19 May 2020, 07:30
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A sequence S consists of 5 distinct positive integers. Are all the integers in the sequence divisible by 5?

(1) The sum of all the integers in the sequence is divisible by 5.
{1,3,5,7,9} => NO
{5,15,25,35,45} => YES

(2) The product of all the integers in the sequence is divisible by 5 but not by 10.
{1,3,5,7,9}=> NO
{5,15,25,35,45} => YES

combining 1 and 2,
{1,3,5,7,9}=> NO
{5,15,25,35,45} => YES

correct answer E
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A sequence S consists of 5 distinct positive integers. Are all the int 19 May 2020, 13:01
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Bunuel
A sequence S consists of 5 distinct positive integers. Are all the integers in the sequence divisible by 5?

(1) The sum of all the integers in the sequence is divisible by 5.
(2) The product of all the integers in the sequence is divisible by 5 but not by 10.

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1) When the sequence is (5,10,15,20,25), the answer is yes. when the sequence is (5, 11, 14, 19, 26),the answer is no.
2) the sequence consists of only odd integers, at least one of them is divisible by 5. no more info. not sufficient
Together, when the sequence is (1, 3, 5, 7, 9), it satisfies both statement. again when the sequence is (5, 15, 25, 35, 45), it meets both conditions. Not sufficient
E is the answer
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A sequence S consists of 5 distinct positive integers. Are all the int 11 Oct 2022, 22:36
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Let's say S = {a, b, c, d, e}. We want to know if all the numbers in the sequence are divisible by 5.

----------------
What does A tell us?
----------------

Let n be some positive integer; a + b + c + d + e = 5n

This is one where we are better off using counterexamples

Let's take the following integers (each with remainder 1) as an option:
a = 1
b = 6
c = 11
d = 16
e = 21

Note that the sum of these numbers is divisible by 5, but none of a,b,c,d,e are themselves divisible by 5.

But we could consider an alternative example:
a = 5
b = 10
c = 15
d = 20
e = 25

This works, so we can establish that Statement A is insufficient.


--------------
What does B tell us?
--------------

Product is divisible by 5 but not by 10; this tell us none of the numbers in the sequence are even.

Algebraically, this says to us that, for some integer m, a * b * c * d * e = 5m, where none of a, b, c, d, e is even.

This is one where we can build a counterexample.

Suppose the following is true:
a = 1
b = 3
c = 5
d = 7
e = 9

The product of these is 945, which is divisible by 5 but not 10; only c is divisible by 5

But we could also consider the alternative here:
a = 5
b = 15
c = 25
d = 35
e = 45

The product of these numbers is a big number divisible by 5 but not 10; and each of a,b,c,d,e is divisible by 5

So Statement B is insufficient

-----------
What if they're both true?
-----------

We can repurpose our last example here:
a = 5
b = 15
c = 25
d = 35
e = 45

Here, each of the numbers of the sequence is divisible by 5 and odd, so it follows that the product is divisible by 5 (but not 10) and the sum of the sequence is divisible by 5

But we can come up with another counterexample here:
a = 1
b = 5
c = 15
d = 3
e = 11

Well, turns out the sum and the product of these are divisible by 5 (but not 10), but only b and c are divisible by 5.

So the statements together are insufficient

-------
The answer is E
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A sequence S consists of 5 distinct positive integers. Are all the int 18 Nov 2023, 10:15
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