P, Q, R, S, T are five distinct positive multiples of 10 suc

Question

P, Q, R, S, T are five distinct positive multiples of 10 such that P < Q < R < S < T. These five numbers have a median of 100 and a range of 60. What is the value of T?

(1) Ratio of P:T is greater than 7:13.

(2) Q is not 80.

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WizakoBaskar · Accepted Answer

Data is sufficient if we can get a UNIQUE value for T from the statements.

Key information from question stem 
1. 5  distinct  multiples of 10.
2. P < Q < R < S < T.
3. Median of these 5 numbers is R = 100.
4. Range (T - P) = 60

Possible values for the set of numbers.  
Because R is 100 and the numbers are distinct multiples of 10, the least possible value for S will be 110 and for T will be 120. Consequently, least value for P is 60.
Because R is 100 and the numbers are distinct multiples of 10, the maximum possible value for Q will be 90 and for P will be 80. Consequently, the maximum value for T will be P + 60 = 80 + 60 = 140.

So, T can take the following values: 120, 130, or 140

Statement 1 : Ratio of P:T is greater than 7:13
If T is 130, then P will be 70 and the ratio will be 7 : 13.
But the ratio is  greater  than 7 : 13. For proper fractions, adding the same positive number to both the numerator and denominator will increase the value of the fraction.
So, if we add 10 to both P and T, we will get P = 80 and T = 140. In this case P : T will be 8 : 14 which is greater than 7 : 13.
That is the maximum value that T can take and therefore, the only that value will satisfy statement 1.

Extending the logic, if we subtract the same positive number from both the numerator and denominator of a proper fraction, the value of the fraction will decrease. So, choosing any value for P and T that are less than 70 and 130 respectively will not result in the ratio having a value greater than 7 : 13.

We can conclude that value of T is 140. 
Statement 1 ALONE is sufficient.

Statement 2 : Q is not 80
From the list of values that T can take, we can deduce that P can take the following values: P could be 60 or 70 or 80.
 Possibility 1 : If P is 60, Q could be 70 or 90 and T will be 120.
 Possibility 2 : If P is 70, Q will be 90 and T will be 130.
 Possibility 3 : If P is 80, Q will be 90 and T will be 140.

In all these 3 possibilities Q is not 80. Ergo, we will not able to find a unique value for T from statement 2. 
Choice A is the answer.

SonalSinha803 · Answer

According to the question, R = 100. Therefore, P = 60 or 70 or 80.
T = 120 or 130 or 140.

1. P:T > 7:13. Therefore, P has be 80 and T has to be 140. 80/140 = 0.57 > 0.53(70/130) and 0.5(60/120).
Sufficient.

2. Insufficient, since it leaves a with two other options from which elimination criteria is not mentioned.

Thus, imo A.

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CareerGeek · Answer

P < Q < R < S < T and Median = R = 100 Range = 60 --> T - P = 60 T should be 120 or more and P should be 80 or less. Lets see possible values which would give a range 60 If P = 80, T = 140 If P = 70, T = 130 If P = 60, T = 120 So, 3 values of T are possible (1) Ratio of P:T is greater than 7:13. If P = 80, T = 140 {P:T = 8:14 > 7:13 - Possible } If P = 70, T = 130 {P:T = 7:13 - Not Possible } If P = 60, T = 120 {P:T = 6:12 < 7:13 - Not Possible } So, T = 140 --> Sufficient (2) Q is not 80 --> Q can be 90 or 70 --> If Q = 90, (P, T) = (80, 140) or (P, T) = (70, 130) 2 values of T are possible So, Insufficient IMO Option A

aviddd · Answer

A. P:T is greater than 7:13

P/T > 7/13

13P > 7T

We know that T = 60+P

13P > 7(60+P)

6P > 420

P > 70

This means P can only be 80. P and Q are distinct and need to be less than 100, so P has to be 80 and Q has to be 90.

Sufficient.

B is insufficient which many people have explained why.

Answer: A

CEdward · Answer

P, Q, R, S, T are five distinct positive multiples of 10 such that P < Q < R < S < T. These five numbers have a median of 100 and a range of 60. What is the value of T?

R is 100
T - P = 60

(1) Ratio of P:T is greater than 7:13.
P is not 70 (and hence T is not 130)
P can only be 80 given the constraints
P cannot be 90 because Q can't be anything.
Sufficient.
(The only thing that took me 3 minutes is figuring out whether 80:140 > 70:130

(2) Q is not 80.
Q can be 90 (and hence P can be 80)
Q can be 70 (and hence P can be 60) 
Insufficient.

A.

KarishmaB · Answer

5 distinct multiplies of 10 with median 100 and range 60. P ___ 100 ___ P+60 The 3 possible values for P and P+60 are: 70 and 130. Q (80/90) and R (110/120) can take multiple values in this case. 60 and 120. Q (70/80/90) and R(110). P=50 or less is not possible because then T = 110 and there is no value for R. 80 and 140. Q (90) and R (110/120/130). P cannot be 90 or more because then there will be no value for Q. (1) Ratio of P:T is greater than 7:13. Ratio of P:T is 7:13 in the case of 70-130. It will be more than 7:13 only in case of 80-140 (10 is added to both numerator and denominator so the ratio moves towards 1 i.e. becomes greater). For more on this, check: https://youtube.com/shorts/xTU-BiP5w_I?feature=shared So T = 140. Sufficient alone. (2) Q is not 80. Q may not be 80 in all 3 cases. We do not get a distinct value of T. Answer (A)

P, Q, R, S, T are five distinct positive multiples of 10 suc

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