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What is the value of t? (1) t(t - 1)^2 = 4t (2) t is an even integer

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Bunuel
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What is the value of t? (1) t(t - 1)^2 = 4t (2) t is an even integer [#permalink] New post   09 Oct 2020, 00:15
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E

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66% (01:37) correct 34% (01:45) wrong based on 428 sessions
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What is the value of t?

(1) t(t - 1)^2 = 4t

(2) t is an even integer.
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C
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QuantMadeEasy
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Re: What is the value of t? (1) t(t - 1)^2 = 4t (2) t is an even integer [#permalink] New post   09 Oct 2020, 01:32
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What is the value of t?

Step 1: Understanding statement 1 alone
(1) t(t - 1)^2 = 4t
t(t - 1)^2 - 4t = 0
t {(t - 1)^2 - 4} = 0
t (t^2 + 1 - 2t -4) = 0
t (t^2 - 2t -3) = 0
t (t^2 -3t + t -3) = 0
t (t-3) (t+1) = 0
Hence, t=-1, 0 or 3
Insufficient

Step 2: Understanding statement 2 alone
(2) t is an even integer.
t = 0, 2, 4....
Insufficient

Step 3: Combining statement 1 and 2
t = 0
Sufficient

IMO C
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Re: What is the value of t? (1) t(t - 1)^2 = 4t (2) t is an even integer [#permalink] New post   08 Jul 2023, 09:57
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kelly_jacques wrote:
Bunuel

I understand this method, but I actually expanded the left side of the equation first, and left 4t on the right side. Thus, I had t^3 -2t^2 + t = 4t. Thereafter, I divided everything (both sides) by t. The problem with that method is that I do not get 0 as a root. I only end up with (t-3)(t+1) at the end. Could you please explain why my methodology is flawed and why we cannot divide by t?

Thank you.


You cannot divide t^3 - 2t^2 + t = 4t by t, or t(t - 1)^2 = 4t, specifically because t can be 0, and we cannot divide by 0. By doing so, you lose a root, namely t = 0.

Never divide an equation by a variable (or an expression containing a variable) unless you are certain that the variable (or the expression with the variable) does not equal zero. Division by zero is not allowed.
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Re: What is the value of t? (1) t(t - 1)^2 = 4t (2) t is an even integer [#permalink] New post   09 Oct 2020, 06:56
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Bunuel wrote:
What is the value of t?

(1) t(t - 1)^2 = 4t

(2) t is an even integer.



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(1) insufic
t(t^2+1-2t)-4t=0, t^3+t-2t^2-4t=0,
t(t^2-2t-3)=0, t[t-3][t+1]=0,
t={3,0,-1}

(2) insufic

(1/2) sufic
t=0

(C)
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Re: What is the value of t? (1) t(t - 1)^2 = 4t (2) t is an even integer [#permalink] New post   09 Oct 2020, 10:39
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Using Statement 1, t can clearly be 0. If t is not zero, we can divide by t on both sides to get (t-1)^2 = 4. If we square something and get 4 as our answer, we must be squaring either 2 or -2. So t-1 must either equal 2 or -2, and t itself must either equal 3 or -1. So we can't find a unique value for t using either Statement alone, but using both, t can only be zero, and the answer is C.
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Re: What is the value of t? (1) t(t - 1)^2 = 4t (2) t is an even integer [#permalink] New post   10 Oct 2020, 09:55
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shanky315 wrote:
Hi Bunuel,
Why is the answer E? using both the statement we can get t=0 (even number ). Please share your solution.

Thanks


The correct answer is C, not E. Edited. Thank you.
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Re: What is the value of t? (1) t(t - 1)^2 = 4t (2) t is an even integer [#permalink] New post   10 Oct 2020, 04:39
@thinkvision711

Can you please help!
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Re: What is the value of t? (1) t(t - 1)^2 = 4t (2) t is an even integer [#permalink] New post   10 Oct 2020, 09:51
Hi Bunuel,
Why is the answer E? using both the statement we can get t=0 (even number ). Please share your solution.

Thanks
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Re: What is the value of t? (1) t(t - 1)^2 = 4t (2) t is an even integer [#permalink] New post   10 Oct 2020, 10:07
Asked: What is the value of t?

(1) t(t - 1)^2 = 4t
If t=3; 3*2^2 = 4*3; t=3 is a solution
t{(t^2 - 2t + 1-4} = 0
t(t^2 - 2t-3) = 0
t(t-3)(t+1) = 0
t = {0,3,-1}
NOT SUFFICIENT

(2) t is an even integer.
Multiple values of t are possible
NOT SUFFICIENT

(1) + (2)
(1) t(t - 1)^2 = 4t
(2) t is an even integer.
t = 0
SUFFICIENT

IMO C
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Re: What is the value of t? (1) t(t - 1)^2 = 4t (2) t is an even integer [#permalink] New post   11 May 2023, 11:16
Bunuel wrote:
shanky315 wrote:
Hi Bunuel,
Why is the answer E? using both the statement we can get t=0 (even number ). Please share your solution.

Thanks


The correct answer is C, not E. Edited. Thank you.



But 0 doesn't come under even/odd category.
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Re: What is the value of t? (1) t(t - 1)^2 = 4t (2) t is an even integer [#permalink] New post   11 May 2023, 11:23
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Alankrita26 wrote:
Bunuel wrote:
shanky315 wrote:
Hi Bunuel,
Why is the answer E? using both the statement we can get t=0 (even number ). Please share your solution.

Thanks


The correct answer is C, not E. Edited. Thank you.



But 0 doesn't come under even/odd category.


ZERO:

1. Zero is an INTEGER.

2. Zero is an EVEN integer. An even number is an integer that is "evenly divisible" by 2, i.e., divisible by 2 without a remainder and as zero is evenly divisible by 2 then it must be even.

3. Zero is neither positive nor negative (the only one of this kind).

4. Zero is divisible by EVERY integer except 0 itself (\(\frac{x}{0} = 0\), so 0 is a divisible by every number, x).

5. Zero is a multiple of EVERY integer (\(x*0 = 0\), so 0 is a multiple of any number, x).

6. Zero is NOT a prime number (neither is 1 by the way; the smallest prime number is 2).

7. Division by zero is NOT allowed: anything/0 is undefined.

8. Any non-zero number to the power of 0 equals 1 (\(x^0 = 1\))

9. \(0^0\) case is NOT tested on the GMAT.

10. If the exponent n is positive (n > 0), \(0^n = 0\).

11. If the exponent n is negative (n < 0), \(0^n\) is undefined, because \(0^{negative}=0^n=\frac{1}{0^{(-n)}} = \frac{1}{0}\), which is undefined. You CANNOT take 0 to the negative power.

12. \(0! = 1! = 1\).
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Re: What is the value of t? (1) t(t - 1)^2 = 4t (2) t is an even integer [#permalink] New post   08 Jul 2023, 09:16
Bunuel

I understand this method, but I actually expanded the left side of the equation first, and left 4t on the right side. Thus, I had t^3 -2t^2 + t = 4t. Thereafter, I divided everything (both sides) by t. The problem with that method is that I do not get 0 as a root. I only end up with (t-3)(t+1) at the end. Could you please explain why my methodology is flawed and why we cannot divide by t?

Thank you.

QuantMadeEasy wrote:
Quote:
What is the value of t?

Step 1: Understanding statement 1 alone
(1) t(t - 1)^2 = 4t
t(t - 1)^2 - 4t = 0
t {(t - 1)^2 - 4} = 0
t (t^2 + 1 - 2t -4) = 0
t (t^2 - 2t -3) = 0
t (t^2 -3t + t -3) = 0
t (t-3) (t+1) = 0
Hence, t=-1, 0 or 3
Insufficient

Step 2: Understanding statement 2 alone
(2) t is an even integer.
t = 0, 2, 4....
Insufficient

Step 3: Combining statement 1 and 2
t = 0
Sufficient

IMO C
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Re: What is the value of t? (1) t(t - 1)^2 = 4t (2) t is an even integer [#permalink]
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