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Harshit4232
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Practice Questions Chat 20 Jan 2024, 23:23
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Option 2 cannot be sufficient to find thr value of a_{5}
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Just solved it. Option 2 is also sufficient, since

a14 = a13 - a12 = 1

Substitute a13 = a12 - a11

a14 = a12 - a11 - a12 = -a11

a14 = -a11

When you extrapolate it, a14 = -a11 = a8 = -a5 which is equal to 1.

Gap of 3 with sign reversal, therefore a5 = -1
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Practice Questions Chat 20 Jan 2024, 23:35
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yashnakhare
Just solved it. Option 2 is also sufficient, since a14 = a13 - a12 = 1 Substitute a13 = a12 - a11 a14 = a12 - a11 - a12 = -a11 a14 = -a11 When you extrapolate it, a14 = -a11 = a8 = -a5 which is equal to 1. Gap of 3 with sign reversal, therefore a5 = -1
Shouldn’t you get the answers from both as same for both options to be sufficient .
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Answer is D, Each statement alone is sufficient right?
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do-both-sufficient-statements-provide-the-same-answer-in-a-ds-question-135812.html

Explained here by bunel.

You should get both answers as 3. If you are not getting then I think you are doing something wrong with second statement. I think second statement is not sufficient. Answer should be A.
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yashnakhare
A sequence a_n defined such that a_{n} = a_{n-1} - a_{n-2} ,where n are integers greater than 2. What is the value of a_5 ?

(1) a_{4} - a_{3} = 3
(2) a_{14} = 1

How is option 2 sufficient

A sequence \(a_n\) defined such that \(a_{n} = a_{n-1} - a_{n-2}\), where n is a positive integer greater than 2. What is the value of \(a_5\)?

    \(a_{3} = a_{2} - a_{1}\);
    \(a_{4} = a_{3} - a_{2} = (a_{2} - a_{1}) - a_{2} = -a_{1}\);
    \(a_{5} = a_{4} - a_{3} = (-a_{1}) - (a_{2} - a_{1}) = -a_{2}\);
    \(a_{6} = a_{5} - a_{4} = (-a_{2}) - (-a_{1})=-(a_{2} - a_{1}) = -a_{3}\);
    \(a_{7} = a_{6} - a_{5} = -(a_{2} - a_{1}) - (-a_{2})=a_{1} = -a_{4}\);
    \(a_{8} = a_{7} - a_{6} = a_{1} - (a_{1} - a_{2})=a_{2} = -a_{5}\);
    and so on.

(1) \(a_{4} - a_{3} = 3\)

Above we we got that \(a_{5} = a_{4} - a_{3}\), hence \(a_{5} = 3\). Sufficient.

(2) \(a_{14} = -3\)

\(a_{14} = -a_{11}=a_8=-a_5=-3\). Hence \(a_{5} = 3\). Sufficient.

Answer: D.
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Bunuel
A sequence \(a_n\) defined such that \(a_{n} = a_{n-1} - a_{n-2}\), where n is a positive integer greater than 2. What is the value of \(a_5\)?
    \(a_{3} = a_{2} - a_{1}\); \(a_{4} = a_{3} - a_{2} = (a_{2} - a_{1}) - a_{2} = -a_{1}\); \(a_{5} = a_{4} - a_{3} = (-a_{1}) - (a_{2} - a_{1}) = -a_{2}\); \(a_{6} = a_{5} - a_{4} = (-a_{2}) - (-a_{1})=-(a_{2} - a_{1}) = -a_{3}\); \(a_{7} = a_{6} - a_{5} = -(a_{2} - a_{1}) - (-a_{2})=a_{1} = -a_{4}\); \(a_{8} = a_{7} - a_{6} = a_{1} - (a_{1} - a_{2})=a_{2} = -a_{5}\); and so on.
(1) \(a_{4} - a_{3} = 3\) Above we we got that \(a_{5} = a_{4} - a_{3}\), hence \(a_{5} = 3\). Sufficient. (2) \(a_{14} = -3\) \(a_{14} = -a_{11}=a_8=-a_5=-3\). Hence \(a_{5} = 3\). Sufficient. Answer: D.
So answer is D when a14 = -3. What if a14 = 1. In that case, from both statements we are getting an answer but a different one. So will the question becomes invalid or we answer A or D?
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aditya.khare
Bunuel
A sequence \(a_n\) defined such that \(a_{n} = a_{n-1} - a_{n-2}\), where n is a positive integer greater than 2. What is the value of \(a_5\)?
    \(a_{3} = a_{2} - a_{1}\); \(a_{4} = a_{3} - a_{2} = (a_{2} - a_{1}) - a_{2} = -a_{1}\); \(a_{5} = a_{4} - a_{3} = (-a_{1}) - (a_{2} - a_{1}) = -a_{2}\); \(a_{6} = a_{5} - a_{4} = (-a_{2}) - (-a_{1})=-(a_{2} - a_{1}) = -a_{3}\); \(a_{7} = a_{6} - a_{5} = -(a_{2} - a_{1}) - (-a_{2})=a_{1} = -a_{4}\); \(a_{8} = a_{7} - a_{6} = a_{1} - (a_{1} - a_{2})=a_{2} = -a_{5}\); and so on.
(1) \(a_{4} - a_{3} = 3\) Above we we got that \(a_{5} = a_{4} - a_{3}\), hence \(a_{5} = 3\). Sufficient. (2) \(a_{14} = -3\) \(a_{14} = -a_{11}=a_8=-a_5=-3\). Hence \(a_{5} = 3\). Sufficient. Answer: D.
So answer is D when a14 = -3. What if a14 = 1. In that case, from both statements we are getting an answer but a different one. So will the question becomes invalid or we answer A or D?

Remember, on the GMAT, two data sufficiency statements always provide true information, and these statements never contradict each other or the stem. If the statements contradict each other, then, as per GMAT standards, the question is flawed. Hence, for the options not to contradict, \(a_{14}\) must be -3 in statement (2). Alternatively, if \(a_{14} = 1\), then in statement (1), \(a_{4} - a_{3}\) must be -1. In either case, though, each statement is sufficient on its own.
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Can someone please help me with these two questions?
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udit0610
Can someone please help me with these two questions?
Is it π-2/ π for 20?
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I recommend checking our NEW GMAT Club Tests Questions:

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Practice Questions Chat 21 Jan 2024, 13:27
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Any solutions for this?
probability-424712.html
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Idk if it right but what i did is

found out probability of getting award is 3/8

and probably of 2 women getting award become 2/4*3/8 + probability of 3 women getting award is 3/4*3/8

result is 15/32 which is like 1/2

we cant award more than 3 women
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8 people need to be selected for 3 positions. So 56 ways .
2 women 1 men - 24
3 women 0 men - 4
Probability = 28/56 = 1/2. Lemme know if it’s wrong
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Four men and four women participated in a dance competition. Top three performers were awarded a gold coin, a silver coin, and a bronze coin, respectively. If there were no ties, what is the probability that at least two women were awarded?

A. 1/4
B. 1/3
C. 1/2
D. 3/4
E. 4/5

    P(at least two women) = P(two women) + P(three women) =

    = 4C2*4C1/8C3 + 4C3/8C3 =

    = 6*4/56 + 4/56 =

    = 1/2.

Answer: C.

Alternatively, note that we can have the following four cases:

    WWW
    WWM
    WMM
    MMM

We need to find the combined probability of the green events. Since there are an equal number of men and women, because of the symmetry, the probability of the green events equals the probability of the red events. And since their sum is 1, then the probability of each, red and green events, is 1/2.

Answer: C.
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Bunuel
I recommend checking our NEW GMAT Club Tests Questions:


One more GMAT club Tests question. This one is a Word Problem. Check it out!

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Data Sufficiency Butler: January 2024
January 22DS 1DS 2
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January 22PS 1PS 2
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Hi, can anyone help me solve this question? And what category/type of math question is this?
"Of the three-digit positive integers, how many have 0 in at least one digit."
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