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# What is the sum of T, U and V? If P, Q, R, S, T, U and V are distinct

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What is the sum of T, U and V? If P, Q, R, S, T, U and V are distinct  [#permalink]

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29 Sep 2018, 09:47
3
00:00

Difficulty:

95% (hard)

Question Stats:

18% (02:21) correct 82% (02:37) wrong based on 39 sessions

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Weekly Quant Quiz Question -10

If the given addition is correct, what is the sum of T, U and V?
P, Q, R, S, T, U and V are distinct digits.

Attachment:

Gmatbusters Quiz -2.jpeg [ 45.31 KiB | Viewed 612 times ]

a) P, Q and R are consecutive odd integers.
b) T = 2

ONLY THE TEXT SOLUTIONS ARE ALLOWED

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What is the sum of T, U and V? If P, Q, R, S, T, U and V are distinct  [#permalink]

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29 Sep 2018, 22:11

Official Solution:

Statement 1:
This statement yields three possibilities for P, Q, and R, in some order: {1, 3, 5}, {3, 5, 7}, {5, 7, 9}; it makes no difference which of P, Q, and R is which digit, because they are all added together.
• If P, Q, and R are 1, 3, and 5 (in whatever order), then the digit T must be 1. This means the digits aren't distinct, so it is impossible.
• If P, Q, and R are 3, 5, and 7 (in whatever order), then T= I. That means S is one of the leftover digits O, 2, 4 6, 8, 9. If these values are plugged into S one at a time, the only one that yields all distinct digits is S -4 (34 + 54+74=162).
• If P, Q, and R are 5, 7, and 9 (in whatever order), then T = 2. That means S is one of the leftover digits O, 1, 3, 4, 6, 8. If these values are plugged into S one at a time, the only one that yields all distinct digits is S = 8 (58 + 78 + 98 = 234).
• Therefore, there are only two possible values of TUV: 162 and 234. In both cases, the sum of T, U, and V is 9,
so (I) is sufficient.

Statement 2:
If T = 2, then trial and error will yield a number of working sets of digits yielding different values for TUV. Examples: 58 + 68 + 78 = 204 (T+ U + V = 6); 41 + 71 + 91 203 ( T+ U + V = 5); 49+69 +89 207 (T+ U + V = 9); and several others.
Therefore, (2) is insufficient.

gmatbusters wrote:

Weekly Quant Quiz Question -10

If the given addition is correct, what is the sum of T, U and V?
P, Q, R, S, T, U and V are distinct digits.

Attachment:
Gmatbusters Quiz -2.jpeg

a) P, Q and R are consecutive odd integers.
b) T = 2

ONLY THE TEXT SOLUTIONS ARE ALLOWED

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##### General Discussion
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Re: What is the sum of T, U and V? If P, Q, R, S, T, U and V are distinct  [#permalink]

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29 Sep 2018, 09:56
Consider A, P Q R are consecutive odd integers. For any sets 1,3,5; 5,7,9; 3,5,7 depending on S values, sum of T, U, V varies.

A is not sufficient.

Consider B, if T = 2, P, Q ,R could be any distinct digits and S can vary giving different values for sum of T,U,V. Hence, B is insufficient.

Combine A,B, if T = 2 then P, Q, R must be 5,7,9 in any order and S must be 8 to satisfy the distinct digits condition giving a unique sum of T,U,V to be 2 + 3 +4 = 5

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Re: What is the sum of T, U and V? If P, Q, R, S, T, U and V are distinct  [#permalink]

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29 Sep 2018, 09:57

As per 1) we know the numbers in 10s digit are odd consecutive integers...But this enough is not suffieicient...it can be either 3,5,7 or 5,7,1
As per 2) T=2 . Now this alone does not give any surity. As there can be multiple combinations leading to this

Using Both We know that P,q,R can only be 5,7,1 as any other combination wont give T=2. But still S can take any value and there can be multiple answers.

Hence neither of the statements alone or together are sufficient. Hence the answer is E
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Re: What is the sum of T, U and V? If P, Q, R, S, T, U and V are distinct  [#permalink]

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29 Sep 2018, 09:58
1) insufficient
if s=1 then v=3
letting p, q and r = 5,7 and 9 respectively then t=2 and u=1
sum of t, u and v= 6
but if we assume s= 2
v=8 and now the sum is 11
2) we do not have to prove this one as when we consider 1st equation, the value of T is 2 in both the cases
therefore insufficient
E
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Re: What is the sum of T, U and V? If P, Q, R, S, T, U and V are distinct  [#permalink]

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29 Sep 2018, 10:01
PS
QS
RS
____
TUV

If the given addition is correct, what is the sum of T, U and V?
P, Q, R, S, T, U and V are distinct digits.

a) P, Q and R are consecutive odd integers.
P,Q,R=1,3,5 OR 3,5,7 OR 5,7,9
NOT SUFFICIENT

b) T = 2

THEREFORE THE ANSWER BETWEEN 200 AND 298
P,Q,R COULD BE 6,7,8 OR 7,8,9 NOT SUFFICIENT
BOTH TOGETHE NOT SUFFICIENT
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Re: What is the sum of T, U and V? If P, Q, R, S, T, U and V are distinct  [#permalink]

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Updated on: 29 Sep 2018, 10:05
First of all lets note that P,Q,R,S,T,U,V are all distinct digits.

St 1) P Q R are consecutive odd integers - this does not give us any information about TUV as PQR could be 1,3,5 or 3,5,7 or 5,7,9. Hence St 1. by itself is not sufficient

St 2) T = 2. Not sufficient by itself as many possibilities

We are left with tow options either C or E.

Option (C) is correct as a couple of trial and errors shows 234 is TUV and the whole set-up is 58+78+98 = 234

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Originally posted by Gladiator59 on 29 Sep 2018, 10:01.
Last edited by Gladiator59 on 29 Sep 2018, 10:05, edited 1 time in total.
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Re: What is the sum of T, U and V? If P, Q, R, S, T, U and V are distinct  [#permalink]

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29 Sep 2018, 10:03
E - both not sufficient
a. It can be any consecutive numbers (not sufficient)
b. T = 2 - not sufficient as the previous three numbers -P Q R-can either be (5,7,9 or 7,9,11)

combined S can be 1 or 2 and V = 3 or 6
and P Q R-can either be (5,7,9 or 7,9,11). Still not sufficient
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Re: What is the sum of T, U and V? If P, Q, R, S, T, U and V are distinct  [#permalink]

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29 Sep 2018, 10:09
IMO C

1) NS = possible valid combinations for P,Q.R are (1,3,5) & (5,7,9)
2) Clearly NS
1+2) (5,7,) is valid.......Ans C
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Re: What is the sum of T, U and V? If P, Q, R, S, T, U and V are distinct  [#permalink]

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29 Sep 2018, 12:00
A. PQR are consecutive odd integers . Here. S is not given and PQR can be any combination - 1,3,5 or 3,5,7, each set yielding different results. Hence, not sufficient.

B not sufficient as information about other digits not given

Both,

As T =2, PQR will be 5,7,9 (any order)

However S is not given which will impact the value of U and V. Thus both together are not sufficient.

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Re: What is the sum of T, U and V? If P, Q, R, S, T, U and V are distinct  [#permalink]

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30 Sep 2018, 10:24
gmatbusters wrote:

Official Solution:

Statement 1:
This statement yields three possibilities for P, Q, and R, in some order: {1, 3, 5}, {3, 5, 7}, {5, 7, 9}; it makes no difference which of P, Q, and R is which digit, because they are all added together.
• If P, Q, and R are 1, 3, and 5 (in whatever order), then the digit T must be 1. This means the digits aren't distinct, so it is impossible.
• If P, Q, and R are 3, 5, and 7 (in whatever order), then T= I. That means S is one of the leftover digits O, 2, 4 6, 8, 9. If these values are plugged into S one at a time, the only one that yields all distinct digits is S -4 (34 + 54+74=162).
• If P, Q, and R are 5, 7, and 9 (in whatever order), then T = 2. That means S is one of the leftover digits O, 1, 3, 4, 6, 8. If these values are plugged into S one at a time, the only one that yields all distinct digits is S = 8 (58 + 78 + 98 = 234).
• Therefore, there are only two possible values of TUV: 162 and 234. In both cases, the sum of T, U, and V is 9,
so (I) is sufficient.

Statement 2:
If T = 2, then trial and error will yield a number of working sets of digits yielding different values for TUV. Examples: 58 + 68 + 78 = 204 (T+ U + V = 6); 41 + 71 + 91 203 ( T+ U + V = 5); 49+69 +89 207 (T+ U + V = 9); and several others.
Therefore, (2) is insufficient.

gmatbusters wrote:

Weekly Quant Quiz Question -10

If the given addition is correct, what is the sum of T, U and V?
P, Q, R, S, T, U and V are distinct digits.

Attachment:
Gmatbusters Quiz -2.jpeg

a) P, Q and R are consecutive odd integers.
b) T = 2

ONLY THE TEXT SOLUTIONS ARE ALLOWED

P Q R (3,5,7) s = (2) TUV = 156
Why 32 + 52 + 72 = 156 is not unique?
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Re: What is the sum of T, U and V? If P, Q, R, S, T, U and V are distinct  [#permalink]

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30 Sep 2018, 10:32
Hi
We need to find sum of T, U and V
As per your solution, sum of T, U,V = 1+5+6 =12
Where as official solutions gives the sum = 5 , 6...
Since we are getting more than one value of sum, the sum of T, U and V cannot be find uniquely.
Statement 2 is INSUFFICIENT.

Hope it is clear now.

saban wrote:
gmatbusters wrote:

Official Solution:

Statement 1:
This statement yields three possibilities for P, Q, and R, in some order: {1, 3, 5}, {3, 5, 7}, {5, 7, 9}; it makes no difference which of P, Q, and R is which digit, because they are all added together.
• If P, Q, and R are 1, 3, and 5 (in whatever order), then the digit T must be 1. This means the digits aren't distinct, so it is impossible.
• If P, Q, and R are 3, 5, and 7 (in whatever order), then T= I. That means S is one of the leftover digits O, 2, 4 6, 8, 9. If these values are plugged into S one at a time, the only one that yields all distinct digits is S -4 (34 + 54+74=162).
• If P, Q, and R are 5, 7, and 9 (in whatever order), then T = 2. That means S is one of the leftover digits O, 1, 3, 4, 6, 8. If these values are plugged into S one at a time, the only one that yields all distinct digits is S = 8 (58 + 78 + 98 = 234).
• Therefore, there are only two possible values of TUV: 162 and 234. In both cases, the sum of T, U, and V is 9,
so (I) is sufficient.

Statement 2:
If T = 2, then trial and error will yield a number of working sets of digits yielding different values for TUV. Examples: 58 + 68 + 78 = 204 (T+ U + V = 6); 41 + 71 + 91 203 ( T+ U + V = 5); 49+69 +89 207 (T+ U + V = 9); and several others.
Therefore, (2) is insufficient.

gmatbusters wrote:

Weekly Quant Quiz Question -10

If the given addition is correct, what is the sum of T, U and V?
P, Q, R, S, T, U and V are distinct digits.

Attachment:
Gmatbusters Quiz -2.jpeg

a) P, Q and R are consecutive odd integers.
b) T = 2

ONLY THE TEXT SOLUTIONS ARE ALLOWED

P Q R (3,5,7) s = (2) TUV = 156
Why 32 + 52 + 72 = 156 is not unique?

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Re: What is the sum of T, U and V? If P, Q, R, S, T, U and V are distinct &nbs [#permalink] 30 Sep 2018, 10:32
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