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20 Dec 2022, 07:00
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Difficulty:
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26% (02:07) correct
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12 Days of Christmas GMAT Competition with Lots of Fun
j, 9, k, and m are in arithmetic progression (in the given order) and j, k, and m are in geometric progression (in the given order). What is the value of j*k? (An arithmetic progression or arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant. A geometric progression, also known as a geometric sequence, is a sequence of non-zero numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio.)
(1) The sum of k+3 and 2m is divisible by 5
(2) The sum of j and 9 is greater than the sum of m and k
j, 9, k, and m are in arithmetic progression (in the given order) and j, k, and m are in geometric progression (in the given order). What is the value of j*k? (An arithmetic progression or arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant. A geometric progression, also known as a geometric sequence, is a sequence of non-zero numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio.)
(1) The sum of k+3 and 2m is divisible by 5
(2) The sum of j and 9 is greater than the sum of m and k
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21 Dec 2022, 06:40
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GMATWhiz Official Explanation:
Step 1: Analyse Question Stem:
- Since j, 9, k and m are in AP, we can say:
- o j = 9 – d
o 9
o k = 9 + d
o m = 9 + 2d - Also, since j, k and m are in GP, we can say:
- o (9-d)(9+2d) = (9+d)^2
⇒81 + 9d – 2d^2= 81 + d^2+ 18d
⇒3d^2+ 9d = 0
⇒d^2+ 3d = 0 - So, d = 0 or d = - 3
We need to find the value of jk = (9-d)(9+d)=81-d^2
Step 2: Analyse Statements Independently (And eliminate options) – AD/BCE
Statement 1: The sum of k+3 and 2m is divisible by 5
- According to this statement, k + 3 + 2m = 5k where k is a positive integer
- ⇒9+d+3+2(9+2d)=5k
⇒12+d+18+4d=5k
⇒30+5d=5k - The above equation is satisfied by both d = 0 and d = -3
- So, we do not know the exact value of d and thus the exact value of 81-d^2
Thus, statement 1 alone is not sufficient and we can eliminate options A and D
Statement 2: The sum of j and 9 is greater than the sum of m and k
- According to this statement, 18 – d > 18 + 3d
- ⇒4d < 0
⇒d < 0 - Between d = 0 and d = -3, only d = -3 will satisfy d < 0 and so the value of d is -3
Hence the right answer is Option B.
General Discussion
20 Dec 2022, 07:57
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j,9,k,m are in arthmatic progress so j+k=18
The possible values of j,k is the group of (1,17),(2,16),(3,15),(4,14),(5,13),(6,12),(7,11),(8,10) and (9,9) he
So the possibility of series is here
1,9,17,25
17,9,1,-7
2,9,16,23
16,9,2,-5
3,9,15,21
15,9,3,-3
4,9,14,19
14,9,4,-1
5,9,13,17
13,9,5,1
6,9,12,15
12,9,6,3
7,9,11,13
11,9,7,5
8,9,10,11
10,9,8,7
9,9,9,9
Then in the question given thet j,k,m are in geometric pattern
So here are only two possibilities
12,9,6,3
And
9,9,9,9
Now applied statement 1st so we can see it's satisfied both series so it's not able to provide solutions
Now considered 2nd statement then we find its can discrimination in both statements and provide answer of question.
So Ans- B
Posted from my mobile device
The possible values of j,k is the group of (1,17),(2,16),(3,15),(4,14),(5,13),(6,12),(7,11),(8,10) and (9,9) he
So the possibility of series is here
1,9,17,25
17,9,1,-7
2,9,16,23
16,9,2,-5
3,9,15,21
15,9,3,-3
4,9,14,19
14,9,4,-1
5,9,13,17
13,9,5,1
6,9,12,15
12,9,6,3
7,9,11,13
11,9,7,5
8,9,10,11
10,9,8,7
9,9,9,9
Then in the question given thet j,k,m are in geometric pattern
So here are only two possibilities
12,9,6,3
And
9,9,9,9
Now applied statement 1st so we can see it's satisfied both series so it's not able to provide solutions
Now considered 2nd statement then we find its can discrimination in both statements and provide answer of question.
So Ans- B
Posted from my mobile device
