a, b, c and d are consecutive integers such that the product

yes, possibility of negative numbers

Yes thats the mean little trick there. You will have to consider the negative numbers too.

In that case, answer should be E because with stmt 1 again, d value is either 7 or -7.

d is a prime number, so it cannot be -7. Only positive integers can be primes (the smallest prime is 2).

Hi Bunuel,

Does that mean the anwer is wrong.

___________________
No, the answer is still A.

The product of consecutive integers a, b, c, and d is 5,040. What is the value of d?

(1) d is prime

(2) d < c < b < a

Given product of consecutive integers a, b, c, and d is 5,040 then we get 7 * 8* 9* 10..

1. d is prime => and only prime in this series is 7...Sufficient.

2. d < c < b < a then it has to be 7 < 8 < 9 < 10... we get d as 7...Sufficient.

IMO D is the correct answer...Both choices are independently sufficient.

a*b*c*d=5040
also
5040=2^4*3^2*5*7
or,
5040=10*9*8*7


(1) d is prime

d=7 ---sufficient !!

(2) d < c < b < a

d=7 ---sufficient !!

D

Factors of 5,040= 10*9*8*7

(1) d is prime. Only prime number in factors is 7.

Sufficient.

(2) d < c < b < a
d is the smallest number, i.e. 7. Sufficient.

D is the answer

Consecutive integers will be 7,8,9,10 OR -7,-8,-9,-10

Statement 1:d is prime-sufficient-only 7 is prime
Statement 2:D is the smallest:Not sufficient:d can be -10 or 7

Answer A

Unless I missed something the same question was already present and indeed KS15 is right and the answer was A)
Nice one.

a-b-c-and-d-are-consecutive-integers-such-that-the-product-141920.html

abcd = 5040, where a,b,c,d are consecutive integers.
d = ?

1) d is prime
5040 = 7*8*9*10
=> d = 7
Sufficient.

2) a > b > c > d
d = 7 or d = -10
=> a, b, c, d can also be negative consecutive integers.
InSufficient.

A is the answer.

Tricky

x (x+1)(x+2)(x+3) =5040 --- 7<x<10

2^4 *7 *2 * 5 --- hidden in here is 7 * 8 *9 *10

Statement 1

A prime number cannot be negative

suff

Statement 2

Actually, because there are four numbers you could technically have -7

insuff

A

IanStewart
There are 2 scenarios like:
a=10
b=9
c=8
d=7

Or,

a=-7
b=-8
c=-9
d=-10

Sometimes, statement 2 says: a=10 and sometimes a=-7. There are just two contradictory info here! Is the statement 2 lair?

I'm not sure I understand your question. That's what happens almost any time a Statement is insufficient. When a Statement is insufficient, that means there are two (or more) different possible situations which produce two (or more) different answers to the question. The various situations we might have are almost always going to be contradictory (they cannot be simultaneously true). For example, if you have a simple question like:

What is the value of the integer k?
1. 2 < k < 5
2. 3 < k < 6

then from Statement 1, we have two possible situations: k = 3 or k = 4. Those are 'contradictory' in the sense that they cannot both be true at the same time, but there's nothing wrong with that. That just means the information is insufficient (since the answer to the question is different in the two cases).

You might be thinking of a different principle altogether. When you use both Statements together, then the two Statements cannot contradict each other in a real GMAT DS question. There always needs to be (at least) one possible situation using both Statements. So you could never see a question like this:

What is the value of the integer k?
1. 2 < k < 5
2. 7 < k < 9

because using both Statements, k cannot exist. Similarly, in the question in this thread, Statement 1 could not say "a is prime", because while on its own, that Statement is fine (a can be 7 if the letters are in increasing order), using both Statements together, we'd have an impossible situation (there is no way a can be prime if a > b > c > d).

But the question in this thread observes that principle of DS question design. The only objection I have to it is that it uses "d is prime" to convey the information that "d is positive". The GMAT would never do that; any official question about prime numbers will always be restricted to positive numbers alone, since the GMAT never tests concepts related to primes, divisibility, or remainders using negatives, and the test doesn't expect you to understand how those concepts are defined for negative integers.

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