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Re: The product of integers a, b, c, and d is 120. What is the value of in [#permalink]
Expert Reply
KS15 wrote:
Bunuel wrote:
The product of integers a, b, c, and d is 120. What is the value of integer d?

(1) a, b, c, and d are consecutive integers
(2) a > b > c > d

Kudos for a correct solution.


(1) a, b, c, and d are consecutive integers:Sufficient-Only 1 combination is possible,2,3,4,5
(2) a > b > c > d:Insufficient> Answers can be 2,3,4,5 OR 1,3,4,10 etc

Answer A


Hi,
you know the combination but how can you find the value of d out of the four given values.... so A is insuff...
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Re: The product of integers a, b, c, and d is 120. What is the value of in [#permalink]
chetan2u wrote:
KS15 wrote:
Bunuel wrote:
The product of integers a, b, c, and d is 120. What is the value of integer d?

(1) a, b, c, and d are consecutive integers
(2) a > b > c > d

Kudos for a correct solution.


(1) a, b, c, and d are consecutive integers:Sufficient-Only 1 combination is possible,2,3,4,5
(2) a > b > c > d:Insufficient> Answers can be 2,3,4,5 OR 1,3,4,10 etc

Answer A


Hi,
you know the combination but how can you find the value of d out of the four given values.... so A is insuff...


Hello,

Sorry I was very sleepy when I did this. :oops:
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Re: The product of integers a, b, c, and d is 120. What is the value of in [#permalink]
Answer is E

1 tells us 2*3*4*5=120
2 tells us the values could be -2*-3*4*5 or 2 3 4 5 or so on

Both together do not tell anything about the signs so E
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Re: The product of integers a, b, c, and d is 120. What is the value of in [#permalink]
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Expert Reply
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem.
Remember equal number of variables and independent equations ensures a solution.

The product of integers a, b, c, and d is 120. What is the value of integer d?

(1) a, b, c, and d are consecutive integers
(2) a > b > c > d

In the original condition there are 4 variables (a,b,c,d) and 1 equation (a*b*c*d=120). Thus we need 3 more equations to match the number of variables and equations. Since there is 1 each in 1) and 2), D has high probability of being the answer. Using both 1) & 2) together, 2<3<4<5(2*3*4*5=120) but -5<-4<-3<-2(-5*-4*-3*-2=120) leads to d=-5,2. The answer is not unique, and therefore the conditions are not sufficient. Therefore the answer is E


Normally for cases where we need 3 more equations, such as original conditions with 3 variables, or 4 variables and 1 equation, or 5 variables and 2 equations, we have 1 equation each in both 1) and 2). Therefore E has a high chance of being the answer (especially about 90% of 2by2 questions where there are more than 3 variables), which is why we attempt to solve the question using 1) and 2) together. Here, there is 80% chance that E is the answer, while C has 15% chance. These two are the key questions. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since E is most likely to be the answer according to DS definition, we solve the question assuming E would be our answer hence using ) and 2) together. (It saves us time). Obviously there may be cases where the answer is A, B, C or D.
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Re: The product of integers a, b, c, and d is 120. What is the value of in [#permalink]
Bunuel wrote:
The product of integers a, b, c, and d is 120. What is the value of integer d?

(1) a, b, c, and d are consecutive integers
(2) a > b > c > d

Kudos for a correct solution.


Statement 1:
Doesn't provide any information about sign of integers.
INSUFFICIENT

Statement 2:
Just provides order of integers. Doesn't provide any information about integers and their signs.
INSUFFICIENT

Combining statement 1 and 2:
a,b,c and d could be 5,4,3 and 2 or -2,-3,-4,-5 respectively.
gives 2 values of d.
INSUFFICIENT

Answer:-E
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Re: The product of integers a, b, c, and d is 120. What is the value of in [#permalink]
An off topic question, but when GMAC says a,b,c,d are consecutive integers, does it not mean a > b > c > d implicitly? ie., will 4,3,1,2 also be termed as consecutive integers?
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Re: The product of integers a, b, c, and d is 120. What is the value of in [#permalink]
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Bunuel wrote:
The product of integers a, b, c, and d is 120. What is the value of integer d?

(1) a, b, c, and d are consecutive integers
(2) a > b > c > d

Kudos for a correct solution.


Statement (1) : four consecutive integers (2*3*4*5)=120,(-5*-4*-3*-2)=120. So the Statement (1) is insufficient

Statement (2) : a>b>c>d ,Many different number of a,b,c or d can be paced in this order that don't give any specific number of d like 7>6>2>0,2>1>0>-1 etc.So the Statement (2) is insufficient

Together the Two statement can not solve the issue of sign or number order.

So the Correct answer is E.
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Re: The product of integers a, b, c, and d is 120. What is the value of in [#permalink]
oh..yessss good question
I did not think about negative values!!!
definitely E is the answer!
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Re: The product of integers a, b, c, and d is 120. What is the value of in [#permalink]
redone the question.

1. thought right away of the possible negative numbers.
we can have 2*3*4*5
or -2 * -3 * -4 * -5
d can be 5 or -5 or 2 or -2...we don't know the order either...

2. well...since we are not restricted to integers, we can have infinite combinations.

1+2.
d can be 5 or can be -2.

not sufficient.

answer is E.
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Re: The product of integers a, b, c, and d is 120. What is the value of in [#permalink]
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