Set A consists of integers -9, 8, 3, 10, and J; Set B consists of

Question

Set A consists of integers -9, 8, 3, 10, and J; Set B consists of integers -2, 5, 0, 7, -6, and T. If R is the median of Set A and W is the mode of set B, and R^W is a factor of 34, what is the value of T if J is negative?

(A) -2
(B) 0
(C) 1
(D) 2
(E) 5

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Sketchitesh · Answer

Set A ( -9,3,8,10 & J) , if J is negative then Median is 3 (middle value (3rd in this case) of set if they are in ascending order) 
Set B (-6,-2,0,5,7 & T), W is mode, but all elements have occured only once, so T must be either one of the values (-6,-2,0,5,7)
so W=T

R^W is factor of 34 . Factors of 34 = 1,2,17,34 => 
3^W is factor of 34. We can conclude that W=0=T.

B is Correct

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bhargavhhhhhhhh · Answer

Set A = {–9, 8, 3, 10, J}, where J < 0 
⇒ Sorted Set A: {J, –9, 3, 8, 10} 
⇒ Median R = 3

Set B = {–2, 5, 0, 7, –6, T} 
To have a mode, T must match an existing number in Set B

Try each value of T:

T = –2 → W = –2 → 3^(–2) = 1/9 → not a factor of 34 
T = 0 → W = 0 → 3^0 = 1 → 1 is a factor of 34 ✅ 
T = 5 → W = 5 → 3^5 = 243 → not a factor 
T = 7 → W = 7 → 3^7 = 2187 → not a factor 
T = –6 → W = –6 → 3^(–6) = 1/729 → not a factor

Factors of 34 = {1, 2, 17, 34}

Only valid case: 
T = 0 ⇒ W = 0 ⇒ 3^0 = 1 ∈ factors of 34

Answer: (B) 0

Dereno · Answer

Set A consists of integers -9, 8, 3, 10, and J

Set B consists of integers -2, 5, 0, 7, -6, and T

given  J is negative .  This implies -9, -J,  3 , 8, 10 or -J, -9,  3 , 8, 10.

The median R of set A is 3.

W is the mode of set B. The possible values of mode is { -2, 5, 0, 7, -6}.

Moreover,  R^w is a factor of 34 . The factors of 34 = 2*17 = 2*2 = 4.

The four factors of 34 are 1,2,17,and 34.

3^w cannot be 2 or 17 or 34.

The only possibility of 3^w is 1, when w =0

The mode of set B is 0. (i.e.,) the value of T = 0

Ayeka · Answer

Set A consists of integers -9, 8, 3, 10, and J; Set B consists of integers -2, 5, 0, 7, -6, and T. If R is the median of Set A and W is the mode of set B, and R^W is a factor of 34, what is the value of T if J is negative?
Set A = (-9,8,3,10,J) and J is negative, so (-9,J,3,8,10). Hence, median is 3=R.
Set B= (-2,5,0,7,-6,T) T has to have same value as an existing number is set B.

(A) -2 = (3)^(-2)=1/9.....Not a factor of 34.
(B) 0 = (3)^0=1........ A factor of 34.

Answer: B

rohitz98 · Answer

Given Set A = (-9,8,3,10,J) 
  Set B= (-2,5,0,7,-6,T)  
 Also Given R is med of Set A and W is mode of Set B and R^W is a factor of 34

Factors of 34 are 17,2,1

Given   J is negative, Hence Set A becomes (-9,J,3,8,10). Hence, median of Set A R=3

For R^W ie., 3^W to be a factor, W must be equal to 0 
For W to be equal to 0 T must be 0

Hence  Option B

Set A consists of integers -9, 8, 3, 10, and J; Set B consists of

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Set A consists of integers -9, 8, 3, 10, and J; Set B consists of

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

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