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655-705 (Hard)|   Math Related|         
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riyasali
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12 Days of Christmas GMAT Competition - Day 1: A sequence of integers 16 Dec 2024, 10:42
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I went via the answer option method:
1) If S4 = 5, then S5 = 8 (5+3 since 5 is not divisible by 4) and S6 = 10 (8+2 since 8 is divisible by 4). We do not have 10 in the option so eliminate this choice.
2) If S4 = 8, then S5 = 10 (8+2 since 8 is divisible by 4) and S6 = 13 (10+3 since 10 is not divisible by 4) Since we have 13 as an option, went with this answer choice.
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12 Days of Christmas GMAT Competition - Day 1: A sequence of integers 16 Dec 2024, 10:49
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Lets take s4 = 8

s4 is divisible by 4
so s5 = s4 + 2
s5 = 10

s5 is not divisible by 4
so s6 = s5 + 3
s6 = 13

only this pair satisfies

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A sequence of integers is defined using the following logic: If \(s_n\) is divisible by 4, then \(s_{n+1} = s_n + 2\). If \(s_n\) is not divisible by 4, then \(s_{n+1} = s_n + 3\).

Select values for \(s_4\) and \(s_6 \)that are jointly consistent with these conditions. Make only two selections, one in each column.
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12 Days of Christmas GMAT Competition - Day 1: A sequence of integers 16 Dec 2024, 10:53
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Explain please!
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12 Days of Christmas GMAT Competition - Day 1: A sequence of integers 16 Dec 2024, 10:55
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After substituting the values of S4=8
we get S5 = 8+2=10
S6 = 10 + 3 = 13
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A sequence of integers is defined using the following logic: If \(s_n\) is divisible by 4, then \(s_{n+1} = s_n + 2\). If \(s_n\) is not divisible by 4, then \(s_{n+1} = s_n + 3\).

Select values for \(s_4\) and \(s_6 \)that are jointly consistent with these conditions. Make only two selections, one in each column.
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12 Days of Christmas GMAT Competition - Day 1: A sequence of integers 16 Dec 2024, 11:00
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If s4 = 8 which is divisible by 4, then s5 = 8 + 2 = 10; Option B
If s5 = 10 which is not divisible by 4, then s6 = 10 + 3 = 13; Option D
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12 Days of Christmas GMAT Competition - Day 1: A sequence of integers 16 Dec 2024, 11:00
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if s4=5: 5 ..8..10...not in option
if s4=8: 8..10..13...Yes..option available

Ans 8 & 13
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12 Days of Christmas GMAT Competition - Day 1: A sequence of integers 16 Dec 2024, 11:07
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If s4= 8

Then s5= 10 since s4 is divisible by 4

Then s6= 13 since s5 is not divisible by 4.

Therefore, s4= 8 and s6=13
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12 Days of Christmas GMAT Competition - Day 1: A sequence of integers 16 Dec 2024, 11:28
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s4=8 and s6=22

sn+1 in first case can be 2,6,10,14,18,22,26....

sn+1 in second case can be 4,5,6,8,9,10,12.....
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12 Days of Christmas GMAT Competition - Day 1: A sequence of integers 16 Dec 2024, 11:36
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If we take S3 as 5 and s4 as 8

S5 would be 10. Then S6 would be S5+1 = S5+3, as S5 is not divisible by 4. S6 would be 13.

If we start solving for S3. We can arrive at S4 =8 , S6= 13
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12 Days of Christmas GMAT Competition - Day 1: A sequence of integers 16 Dec 2024, 11:44
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In TPA questions its always better to form a strategy first before solving.

The stem tells us that; A sequence of integers is defined using the following logic: If sn is divisible by 4, then sn+1=sn+2 If sn is not divisible by 4, then sn+1=sn+3.

And we have to select values for s4 and s6 that are jointly consistent with these conditions.

To solve this question we have to see if by any chance we can use the options for our advantage.

Let’s assume;
s4=8, and since 8 is divisible by 4,
So, s5= 8+2=10, since 10 is not divisible by 4,
And, S6 = 10+3=13.
So the required values are 8 and 13.

We can also check other options similarly, but since there is only one correct answer, doing so would be obsolete.

Hence fill the respective options here.
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12 Days of Christmas GMAT Competition - Day 1: A sequence of integers 16 Dec 2024, 12:01
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One can substitute values from the options and check which one satisfies.

for eg.- Lets suppose S4=4k, S5 will be 4k +2. S5 will not be divisible by 4 hence S6 will be S5 + 3 i.e. 4K + 5.

From the options, S4=8 and S6=13 satisfies.
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12 Days of Christmas GMAT Competition - Day 1: A sequence of integers 16 Dec 2024, 12:02
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Ans: S4 = 8 and S6 = 13

If S4=5 then S5=8(5+3 since S4 is not a multiple of 4) and S6=10(8+2 since S5 is a multiple of 4)(Not possible as value is not given)
If S4=8 then S5=10(8+2 since S4 is a multiple of 4) and S6=13(10+3 since S5 is not a multiple of 4)

Similarly, if we calculate for values of S4 and S6, we observe that there is only one possible combination i.e., when S4=8, S6=13
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A sequence of integers is defined using the following logic: If \(s_n\) is divisible by 4, then \(s_{n+1} = s_n + 2\). If \(s_n\) is not divisible by 4, then \(s_{n+1} = s_n + 3\).

Select values for \(s_4\) and \(s_6 \)that are jointly consistent with these conditions. Make only two selections, one in each column.
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12 Days of Christmas GMAT Competition - Day 1: A sequence of integers 16 Dec 2024, 12:09
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\(s_n\) is divisible by 4 -> \(s_{n+1} = s_n + 2\)
\(s_n\) is NOT divisible by 4 -> \(s_{n+1} = s_n + 3\)

Assume \(s_{4}\) is \(x\)

Case 1 : \(x\) is divisible by 4

\(s_{5}\) = \(s_{4} + 2 = x + 2 \)

\(s_{5}\) cannot be divisible by 4 (there must be a difference of 4 between two multiples of 4)

\(s_{6} = s_{5} + 3 = x + 5 \)

Case 2 : \(x\) is NOT divisible by 4

\(s_{5}\) = \(s_{4} + 3 = x + 3 \)

\(s_{5}\) maybe divisible by 5. Assuming both cases
a) \(s_{5}\) divisible by 5

\(s_{6} = s_{5} + 2 = x + 5\)

b) \(s_{5}\) is NOT divisible by 5

\(s_{6} = s_{5} + 3 = x + 6\)


So possible options of\( s_{4}\) and\( s_{6}\) are\( (x, x+5)\) and \((x, x+6)\)

Based on options that is only (8, 13)


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A sequence of integers is defined using the following logic: If \(s_n\) is divisible by 4, then \(s_{n+1} = s_n + 2\). If \(s_n\) is not divisible by 4, then \(s_{n+1} = s_n + 3\).

Select values for \(s_4\) and \(s_6 \)that are jointly consistent with these conditions. Make only two selections, one in each column.
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12 Days of Christmas GMAT Competition - Day 1: A sequence of integers 16 Dec 2024, 12:10
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After testing choices we see that if s4=8, s5=8+2=10 and hence s6=10+3=13 which satisfies the given sequence

hence ans is 8,13
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12 Days of Christmas GMAT Competition - Day 1: A sequence of integers 16 Dec 2024, 12:12
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Possible values for
s
4
s
4
​
:

s
4
s
4
​
can be 5, 8, 12, 13, 16, or 22.
Determine
s
5
s
5
​
based on
s
4
s
4
​
:

If
s
4
s
4
​
is divisible by 4, then
s
5
=
s
4
+
2
s
5
​
=s
4
​
+2.
If
s
4
s
4
​
is not divisible by 4, then
s
5
=
s
4
+
3
s
5
​
=s
4
​
+3.
Determine
s
6
s
6
​
based on
s
5
s
5
​
:

If
s
5
s
5
​
is divisible by 4, then
s
6
=
s
5
+
2
s
6
​
=s
5
​
+2.
If
s
5
s
5
​
is not divisible by 4, then
s
6
=
s
5
+
3
s
6
​
=s
5
​
+3.
Evaluate Each Possible
s
4
s
4
​
:
If
s
4
=
5
s
4
​
=5:

s
5
=
5
+
3
=
8
s
5
​
=5+3=8 (since 5 is not divisible by 4)
s
6
=
8
+
2
=
10
s
6
​
=8+2=10 (since 8 is divisible by 4)
s
6
=
10
s
6
​
=10 (not a given option)
If
s
4
=
8
s
4
​
=8:

s
5
=
8
+
2
=
10
s
5
​
=8+2=10 (since 8 is divisible by 4)
s
6
=
10
+
3
=
13
s
6
​
=10+3=13 (since 10 is not divisible by 4)
s
6
=
13
s
6
​
=13 (valid option)
If
s
4
=
12
s
4
​
=12:

s
5
=
12
+
2
=
14
s
5
​
=12+2=14 (since 12 is divisible by 4)
s
6
=
14
+
3
=
17
s
6
​
=14+3=17 (since 14 is not divisible by 4)
s
6
=
17
s
6
​
=17 (not a given option)
If
s
4
=
13
s
4
​
=13:

s
5
=
13
+
3
=
16
s
5
​
=13+3=16 (since 13 is not divisible by 4)
s
6
=
16
+
2
=
18
s
6
​
=16+2=18 (since 16 is divisible by 4)
s
6
=
18
s
6
​
=18 (not a given option)
If
s
4
=
16
s
4
​
=16:

s
5
=
16
+
2
=
18
s
5
​
=16+2=18 (since 16 is divisible by 4)
s
6
=
18
+
3
=
21
s
6
​
=18+3=21 (since 18 is not divisible by 4)
s
6
=
21
s
6
​
=21 (not a given option)
If
s
4
=
22
s
4
​
=22:

s
5
=
22
+
3
=
25
s
5
​
=22+3=25 (since 22 is not divisible by 4)
s
6
=
25
+
3
=
28
s
6
​
=25+3=28 (since 25 is not divisible by 4)
s
6
=
28
s
6
​
=28 (not a given option)
Conclusion:
The only consistent pair of values for
s
4
s
4
​
and
s
6
s
6
​
from the given options is:

s
4
=
8
s
4
​
=8
s
6
=
13
s
6
​
=13
Therefore, the correct selections are:

s4: 8

s6: 13
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12 Days of Christmas GMAT Competition - Day 1: A sequence of integers 16 Dec 2024, 12:36
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If s4 = 8, then s5 = 10 (since 8 is divisible by 4, add 2), and s6 = 13 (since 10 is not divisible by 4, add 3). This pair is consistent with the rules.
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12 Days of Christmas GMAT Competition - Day 1: A sequence of integers 16 Dec 2024, 12:46
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S1 can be 0 (divisible by 4) or 1 (not divisible by 4)

So when S1 = 0; we get S2 = 2, S3 = 5, S4 = 8, S5 = 10 & S6 = 13
& when S1 = 1; we get S2 = 4, S3 = 6; S4 = 9; S5 = 12; & S6 = 14

From the options, only S4 = 8 & S6 = 13 match

Hence, 8 & 13
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A sequence of integers is defined using the following logic: If \(s_n\) is divisible by 4, then \(s_{n+1} = s_n + 2\). If \(s_n\) is not divisible by 4, then \(s_{n+1} = s_n + 3\).

Select values for \(s_4\) and \(s_6 \)that are jointly consistent with these conditions. Make only two selections, one in each column.
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12 Days of Christmas GMAT Competition - Day 1: A sequence of integers 16 Dec 2024, 12:57
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it's like unlocking the right combination to the mystery sequence! 🔑
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12 Days of Christmas GMAT Competition - Day 1: A sequence of integers 16 Dec 2024, 13:00
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  1. If Sn is divisible by 4, then Sn+1=Sn+2 sn+1=sn+2.
  2. If Sn is not divisible by 4, then sn+1=sn+3sn+1=sn+3.


Possible values we are selecting:
  • s4: 5, 8, 12, 13, 16, 22
  • s6: 5, 8, 12, 13, 16, 22

Step-by-Step Explanation:

  1. Case 1: s4 = 8:
    • 8 is divisible by 4 → s5 = s4+2 = 8+2 = 10
    • 10 is not divisible by 4 → s6 = s5+3 = 10+3= 13
    Therefore, s6 = 13 when s4 = 8
  2. Case 2: s4 = 12:
    • 12 is divisible by 4 → s5 = s4+2 = 12+2 = 14
    • 14 is not divisible by 4 → s6 = s5+3 = 14+3 = 17
    Here, s6=17, but 17 is not an option.
  3. Case 3: s4 = 13:
    • 13 is not divisible by 4 → s5 = s4+3 = 13+3 = 16
    • 16 is divisible by 4 → s6 = s5+2 = 16+2 = 18
    Here, s6=18, but 18 is not an option.




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A sequence of integers is defined using the following logic: If \(s_n\) is divisible by 4, then \(s_{n+1} = s_n + 2\). If \(s_n\) is not divisible by 4, then \(s_{n+1} = s_n + 3\).

Select values for \(s_4\) and \(s_6 \)that are jointly consistent with these conditions. Make only two selections, one in each column.
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12 Days of Christmas GMAT Competition - Day 1: A sequence of integers 16 Dec 2024, 13:31
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To make it simple:

____ , ____ , ____
s4 s5 s6

We can work backward here.

first number is 5 -> 5 , 8 , 10 5 is not divisible by 4 so s5= 5+3 = 8. 8 is divisble by 4 so s6 = 8+2 = 10
second number is 8 -> 8 , 10 , 13 8 is divisble by 4 so s6 = 8+2 = 10 10 is not divisible by 4 so s6= 10+3 = 13.

We have our answer s4=8 and s6=13.
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