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Misha is now 3 years older than Tanya. If in 12 years, the sum of thei

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Misha is now 3 years older than Tanya. If in 12 years, the sum of thei  [#permalink]

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New post 31 Jul 2019, 22:43
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Re: Misha is now 3 years older than Tanya. If in 12 years, the sum of thei  [#permalink]

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New post 31 Jul 2019, 23:51
Bunuel wrote:
Misha is now 3 years older than Tanya. If in 12 years, the sum of their ages will be 61, how old is Tanya now ?

A. 16
B. 17
C. 18
D. 19
E. 20


Given:
1. Misha is now 3 years older than Tanya.
2. In 12 years, the sum of their ages will be 61,

Asked: How old is Tanya now ?

Let Tanya be x years old now
Misha is x+3 years old

In 12 years
Tanya will be x+12 years old
Tanya will be x+15 years old

x+12 + x +15 = 61
x = 17
Tanya is 17 years old now

IMO B
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Re: Misha is now 3 years older than Tanya. If in 12 years, the sum of thei  [#permalink]

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New post 01 Aug 2019, 03:21
Let the present ages of Misha and Tanya be M and T years respectively. In 12 years, their respective ages will be M+12 and T+12.

The sum of their ages in 12 years is 61 years. Therefore, M + 12 + T + 12 = 61, which means,

M + T = 37.

From the question statement, we know M = T + 3. Substituting this value of M in the equation above, we have,

T + 3 + T = 37, which gives us T = 17 on simplification. So, Tanya is 17 years old now.

The correct answer option is B.
Hope this helps!
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Re: Misha is now 3 years older than Tanya. If in 12 years, the sum of thei  [#permalink]

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New post 01 Aug 2019, 23:33
Hi,

You can use an alternate approach to solve this question.
Let's assume that Tanya is 18 now (the middle answer choice). If Tanya is 18, Misha is 21 years old. In 12 years, Tanya will be 30 and Misha will be 33. Sum of their ages equal 63. It's not matching. Eliminate C.

It's evident that we should try a smaller number now. Let's try 17.
If Tanya is 17 now, Misha is 20 years old. In 12 years, Tanya will be 29 and Misha will be 32. Sum of their ages equal 61. This is matching. So, the answer is B.


Please give kudos if you liked the solution. :)


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Re: Misha is now 3 years older than Tanya. If in 12 years, the sum of thei  [#permalink]

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New post 02 Aug 2019, 08:26
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OA is provided as E but should be B. Please correct
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Re: Misha is now 3 years older than Tanya. If in 12 years, the sum of thei  [#permalink]

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Misha is now 3 years older than Tanya. If in 12 years, the sum of thei  [#permalink]

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New post 02 Aug 2019, 09:45
Bunuel wrote:
Misha is now 3 years older than Tanya. If in 12 years, the sum of their ages will be 61, how old is Tanya now ?

A. 16
B. 17
C. 18
D. 19
E. 20


The natural first instinct of many of us will be to set up equations and solve for unknown quantity (Tanya's age). In this simple example, that would work very well as the numbers are simple to add/subtract.

For more complex variations of this question, the "plug in" approach is probably better.

Key points that facilitate plug-in approach:


- The answer choices are arranged in ascending (descending) order.

- Start with C, the middle option.


If plug-in results in smaller number, check for answer choices D/E.

If plug-in results in larger nuber, check for answer choices B/A.


In which direction from C should you go (either D/E or B/A) will depend on how much "away" you are from the number stated in the question stem.


For descending answer choices, reverse the approach.
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Re: Misha is now 3 years older than Tanya. If in 12 years, the sum of thei  [#permalink]

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New post 06 Aug 2019, 16:39
Bunuel wrote:
Misha is now 3 years older than Tanya. If in 12 years, the sum of their ages will be 61, how old is Tanya now ?

A. 16
B. 17
C. 18
D. 19
E. 20



Let’s let M = Misha’s current age and T = Tanya’s current age. We can create the equation:

M = 3 + T

In 12 years, Misha will be M + 12, and Tanya will be T + 12 years old. Thus, we have:
M + 12 + T + 12 = 61

M + T = 37

Substituting (3 + T) for M, we have:

3 + T + T = 37

2T = 34

T = 17

Answer: B
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Re: Misha is now 3 years older than Tanya. If in 12 years, the sum of thei   [#permalink] 06 Aug 2019, 16:39

Misha is now 3 years older than Tanya. If in 12 years, the sum of thei

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