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Answer is E

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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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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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
ANSWER=E
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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

Kind Regards,
GLadi
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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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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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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.

Thus, answer is E

Posted from my mobile device
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gmatbusters

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.

Answer A


gmatbusters

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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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
gmatbusters

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.

Answer A


gmatbusters

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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saban
gmatbusters

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.

Answer A


gmatbusters

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?

gmatbusters

This is a possibility as per statement 1 only.

TUV can be (3,5,7)

S can be 2

Then it will yield 156

But 1+5+6=11 ! not 9. Please help
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Recheck your assumption, All P, Q, R, S, T, U, V are distinct.

As per your assumption:

" TUV P, Q, R can be (3,5,7)

S can be 2

Then it will yield 156,

HERE: U and Q both are 5, but these should be distinct
[/color]

hence assumption is invalid.

"

PearlRay

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.

Answer A


gmatbusters

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?[/quote]

gmatbusters

This is a possibility as per statement 1 only.

TUV can be (3,5,7)

S can be 2

Then it will yield 156

But 1+5+6=11 ! not 9. Please help[/quote]
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gmatbusters
Recheck your assumption, All P, Q, R, S, T, U, V are distinct.

As per your assumption:

" TUV P, Q, R can be (3,5,7)

S can be 2

Then it will yield 156,

HERE: U and Q both are 5, but these should be distinct
[/color]

hence assumption is invalid.

"

PearlRay

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.

Answer A


gmatbusters

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?

gmatbusters

This is a possibility as per statement 1 only.

TUV can be (3,5,7)

S can be 2

Then it will yield 156

But 1+5+6=11 ! not 9. Please help[/quote][/quote]

P,Q,R,S,T,U,V all are unique values.
P Q R (3,5,7) s = (2) TUV = 156
Here, Q=U=5 thus not a valid selection.
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On my second go, I somehow didn't take the PS, QS, RS as two digit numbers at all. Rather I considered them to be product of the digits. How can we rule out my possibility with nothing given in the question?
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GMATBusters

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.

Answer A


gmatbusters

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



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.

What if P,Q,R are 1,3,5 and S = 2 , then the sum will yield 96 making T = 0, U = 9 , V = 6 ( This is one set f values possible where T = 0 for P,Q,R as 1,3,5.

And total for T + U + V = 0+9+6 = 15 , a second answer to the obtained from 234 and 162.

Please help, this one case gives a different answer.

In my opinion answer should be (c) , that would exclude 096 and 162 case and leave only 234, giving one unique answer as 9.
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math Expert

What if P,Q,R are 1,3,5 and S = 2 , then the sum will yield 96 making T = 0, U = 9 , V = 6 ( This is one set f values possible where T = 0 for P,Q,R as 1,3,5.

And total for T + U + V = 0+9+6 = 15 , a second answer to the obtained from 234 and 162.

Please help, this one case gives a different answer.

In my opinion answer should be (c) , that would exclude 096 and 162 case and leave only 234, giving one unique answer as 9.
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