a trussian's weight , in Keils , can be calculated by taking the square root of his age in years. A Trussian's teenager now weighs 3 Keils less than he will 17 years after he is twice as old as he is now. How old is he now?
A 14
B 15
C 16
D 17
E 18
5-Day Free Trial
5-day free, full-access trial TTP
Available with Beat the GMAT members only code
MORE DETAILS
algebra
This topic has expert replies
-
vaibhav101
- Master | Next Rank: 500 Posts
- Posts: 138
- Joined: Mon May 01, 2017 11:56 pm
- Thanked: 4 times
-
deloitte247
- Legendary Member
- Posts: 2214
- Joined: Fri Mar 02, 2018 2:22 pm
- Followed by:5 members
Given that ;
Current weight is 3 times less than his weight will be when his age is doubled plus 17.
Let a = current age.
$$Therefore,\ current\ weight\ =\ \sqrt{a}$$
$$\ \sqrt{a}\ +\ 3\ =\ \sqrt{2a\ +\ 17}$$
Square both sides.
$$a\ +\ 6\sqrt{a}\ +\ 9\ =\ 2a\ +\ 17$$
Collect like items
$$a\ -\ 6\sqrt{a}\ +\ 8\ =\ 0$$
$$substituting\ \sqrt{a\ }\ =\ x$$
$$\ x^2\ -\ 6x\ +\ 8\ =\ 0$$
Factorizing ...........
(x - 2) (x - 4) = 0
x = 2 or x = 4.
$$Remember\ that\ x\ =\ \sqrt{a}$$
$$\sqrt{a}\ =\ 2\ or\ \sqrt{a}\ =\ 4$$
Square both sides.
$$\left(\sqrt{a}\right)^2\ =\ 2^2\ or\ \left(\sqrt{a}\right)^2=\ 4^2$$
a = 4 or a = 16
Option C is the correct answer.
Current weight is 3 times less than his weight will be when his age is doubled plus 17.
Let a = current age.
$$Therefore,\ current\ weight\ =\ \sqrt{a}$$
$$\ \sqrt{a}\ +\ 3\ =\ \sqrt{2a\ +\ 17}$$
Square both sides.
$$a\ +\ 6\sqrt{a}\ +\ 9\ =\ 2a\ +\ 17$$
Collect like items
$$a\ -\ 6\sqrt{a}\ +\ 8\ =\ 0$$
$$substituting\ \sqrt{a\ }\ =\ x$$
$$\ x^2\ -\ 6x\ +\ 8\ =\ 0$$
Factorizing ...........
(x - 2) (x - 4) = 0
x = 2 or x = 4.
$$Remember\ that\ x\ =\ \sqrt{a}$$
$$\sqrt{a}\ =\ 2\ or\ \sqrt{a}\ =\ 4$$
Square both sides.
$$\left(\sqrt{a}\right)^2\ =\ 2^2\ or\ \left(\sqrt{a}\right)^2=\ 4^2$$
a = 4 or a = 16
Option C is the correct answer.
GMAT/MBA Expert
-
Scott@TargetTestPrep
- GMAT Instructor
- Posts: 7273
- Joined: Sat Apr 25, 2015 10:56 am
- Location: Los Angeles, CA
- Thanked: 43 times
- Followed by:29 members
We can let his current age = x and create the following equation:vaibhav101 wrote:a trussian's weight , in Keils , can be calculated by taking the square root of his age in years. A Trussian's teenager now weighs 3 Keils less than he will 17 years after he is twice as old as he is now. How old is he now?
A 14
B 15
C 16
D 17
E 18
√x = √(2x + 17) - 3
√x + 3 = √(2x + 17)
Squaring both sides, we have:
x + 6√x + 9 = 2x + 17
6√x = x + 8
Squaring both sides again, we have:
36x = x^2 + 16x + 64
x^2 - 20x + 64 = 0
(x - 4)(x - 16) = 0
x = 4 or x = 16
Since only 16 is given in the answer choices, then C is the correct choice.
Alternate solution:
Since the problem involves taking the square root of a number, and 16 is the only number in the answer choices that is a perfect square, we can guess that 16 is the correct answer. We only need to verify that it is the correct answer.
If the Trussian's current age is 16, then his weight would be √16 = 4 Keils.
17 years after he is twice as old, his age will be 17 + 2(16) = 49 and his weight will be √49 = 7 Keils.
Since 4 is 3 less than 7, we see that we have guessed correctly.
Answer: C
Scott Woodbury-Stewart
Founder and CEO
[email protected]
See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews
