Mary and Ket are cousins.Mary's present age is 9 times what

Question

Mary and Ket are cousins. Mary's present age is 9 times what Ket's age 12 years ago was. When Ket will be 17 years older than Mary's present age, the sum of their ages will be 100. The present ages of Mary and Ket, respectively are

A. 27 and 15
B. 36 and 18
C. 18 and 14
D. 30 and 16
E. none of these

A. 27 and 15
B. 36 and 18
C. 18 and 14
D. 30 and 16
E. none of these

mikemcgarry · Answer

Dear mannava189 , This is probably a notch harder than what the GMAT would ask, but I'm happy to show the solution. Use the variables M = Mary's current age K = Ket's current age what Ket's age 12 years ago was = (K - 12) Thus, the first math sentence says M = 9(K - 12) M = 9K - 108 --- equation #1 The next sentence is tricky. 17 years older than Mary's present age = (M + 17) When will K be that old? In ((M + 17) - K) years; at that time .... Ket's age will be (M + 17) Mary's age will be M + ((M + 17) - K) = 2M - K + 17 and the sum of their ages will be 100, so (M + 17) + (2M - K + 17) = 100 3M - K + 34 = 100 3M = K + 66 --- equation #2 Now, multiply both sides of equation #1 by 3, so that we set equal the quantities equal to 3M ---- 3M = 27K - 324 3M = K + 66 therefore 27K - 324 = K + 66 27K = K + 66 + 324 = K + 390 26K = 390 K = 15 If K = 15, then M = 9(15 - 12) = 9*3 = 27 Mary is 27 and Ket is 15. Answer = (A) Both the calculation there, as well as interpreting the wording, is a little beyond what the GMAT expects, but does all this make sense? Mike :-)

b2bt · Answer

By plugging the options you can eliminate B and D  
e.g. B) 36 and 18. 18 - 12 = 6. 6*9 = 54 not equal to Mary's present age.

You get option A and D. Out of which A looks better (coz Ket's age is around 44 so M + K is close to 100). I would mark A and move ahead. Little bit risk involved but would rather take it.

SVaidyaraman · Answer

1. Let M amd K be the present age of Mary and Ket respectively
2. M=9(k-12) or M-9k= -108 ---- (1)
3. When Ket is 17 years older than Mary, Ket's age at that time will be M+17
4. Mary's age at that time will be Ket's age which is M+17 plus the difference between Mary's and Ket's age which we will take as M-K
5. We have at that time the sum of their ages being 100 i.e., (M+17 + M-K) + M+17 =100 or 3M-K=66 ----- (2)
6. Solving (1) and (2), we have M=27 and K=15.

ScottTargetTestPrep · Answer

We can analyze the given answer choices A to D.

A) 27 and 15

We see that 27 = 9 x (15 - 12). So Mary could be 27 and Ket could be 15. When Ket is 27 + 17 = 44 years old, she will be 44 - 15 = 29 years older and Mary will be 29 years older too, so Mary’s age will be 27 + 29 = 56. If we add 44 and 56, we have 100. So A is the correct answer.

Answer: A

shivani1351 · Answer

Let Mary's and Ket's present ages be M and K respectively.
Ket's age 12 years ago would be K-12.
Hence, M = 9(K-12) = 9K-108
Thus, M = 9K-108

Now, coming to the second part of the question:
Ket's age = M+17 (as the condition given is that Ket is 17 years older than Mary's current age in this case)
We need to find out how many years have passed between this scenario and the earlier one to calculate their ages.

No. of years passed = M+17-K = 9K-108+17-K = 8K-91

Thus, Mary's age would now be M+8K-91.

Since the sum of both their ages is given as 100 : M+8K-91+M+17 = 100

18K-216+8K-74 = 100

Solving, we get K = 15
As M = 9K-108 = 27

Hence, the present ages of Mary and Ket, respectively are 27 and 15 (Option A)

temporeincidunt · Answer

Correct answer: A. 27 and 15  
 Why A is right 
 
   Check the first condition: 
Ket’s age 12 years ago = 15−12=315−12=3.
Mary’s present age = 9×3=279×3=27 ✔️  
   Check the second condition: 
Ket will be  17 years older than Mary’s present age  when Ket is 27+17=4427+17=44.
Years from now = 44−15=2944−15=29.
Then Mary’s age = 27+29=5627+29=56.
Sum = 44+56=10044+56=100 ✔️
Both conditions are satisfied.

Adit_ · Answer

You can just subtract the second number by 12 and check if first is 9x the second, only A solves the problem. The answer now is either E or A only, now 27+17=44 and the other would be 56 same time so 56+44=100 hence this too is satisfied.
A is the answer.

Aditya_Singh · Answer

K and M have “x” years of age difference between them. Now as per the first statement The present age of M would be 9(K-12) and of K would be K

...(1) thus difference in their ages here would be 9K - 108 - K = x Or “x = 8K - 108” ...(2) The second statement states, when K would be M + an additional 17 years so (M+17) and M would the additional 17 years + their age difference (x) Their Sum would be 100. So (M+17) + (M+17+x) = 100 2(M+17) + x = 100 From statement 1 and (2) 2(9K - 108 + 17) + 8K - 108 = 100 18K - 182 + 8K - 108 = 100 26K = 390 K would be 15, putting this in first statement M would be 27

HarshavardhanR · Answer

https://gmatclub.com/forum/download/file.php?id=87708 --- Harsha GMAT-Club-Forum-bp73hxk0.png

Mary and Ket are cousins.Mary's present age is 9 times what

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Mary and Ket are cousins.Mary's present age is 9 times what

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