If x = (y)(y + 1) and y is a prime number less than 11, which of the f

[quote="duahsolo"]If x = (y)(y + 1) and y is a prime number less than 11, which of the following could not be the product of 2 consecutive integers?

Given y is a prime number less than 7
so y can be 2 3 5 7
x=y*(y+1)
so x can be 6 12 30 56

So from options
A. 5x can be (5*6)
B. 11x can be (11*12)
C. 13x can be (13*12)
D. 23x cannot be
E. 57x can be (56*57)
So answer option D.

Since y is a prime number less than 11, there are only 4 possible vales for y.
y COULD equal 2, 3, 5 or 7

This also means there are only 4 possible vales for x.

x = (y)(y + 1)

If y = 2, then x = (2)(2 + 1) = 6
If y = 3, then x = (3)(3 + 1) = 12
If y = 5, then x = (5)(5 + 1) = 30
If y = 7, then x = (7)(7 + 1) = 56

Now let's check each answer choice...
a) Can 5x be the product of 2 consecutive integers?
Yes. When x = 6, then 5x = 5(6) = 30
So, 5x CAN BE the product of 2 consecutive integers (5 and 6)
ELIMINATE A

b) Can 11x be the product of 2 consecutive integers?
Yes. When x = 12, then 11x = 11(12)
So, 11x CAN BE the product of 2 consecutive integers (11 and 12)
ELIMINATE B

c) 13x
When x = 12, then 13x = 13(12)
So, clearly, 13x CAN BE the product of 2 consecutive integers (12 and 13)
ELIMINATE C

e) 57x
When x = 56, then 57x = 57(56)
So, clearly, 57x CAN BE the product of 2 consecutive integers (56 and 57)
ELIMINATE E

By the process of elimination, the correct answer is D

Cheers,
Brent

Given y is a prime number less than 11
possible values of y are 2 3 5 7
given, x=y*(y+1)
if y = 2 x=2*3=6
if y = 3 x=3*4=12
if y = 5 x=5*6=30
if y = 7 x=7*8=56

so possible values of x are 6,12,30,56

So from options
A. 5x can be (5*6)
B. 11x can be (11*12)
C. 13x can be (13*12)
D. 23x cannot be
E. 57x can be (56*57)
So answer option D.

I hope it helps.

x = (y)(y+1)

y=2 --> x=6
y=3 --> x=12
y=5 --> x=30
y=7 --> x=56

A. 5(6) - ELIMINATE
B. 11(12) - ELIMINATE
C. 13(12) - ELIMINATE
D. 23(#) --> CORRECT!! We don't have a value of x that is a consecutive integer with 23
E. 57(56) - ELIMINATE

If x = (y)(y + 1) and y is a prime number less than 11, which of the following could not be the product of 2 consecutive integers?

A. 5x
B. 11x
C. 13x
D. 23x
E. 57x
_________________

Since y is prime number it can take only following values: 2, 3,5,7,11
For these values x equals to
2*3 =6
Or 3*4 =12
Or 5*6= 30
Or 7*8= 56
Or 11*12 =132

Ans = (d)

Sent from my Redmi Note 3 using GMAT Club Forum mobile app

why not 13x or 57x ? What am i missing here ?

There are not many prime numbers less than 11, so let’s list them: 2, 3, 5, and 7. Thus x could be any one of the following numbers:

If y = 2, then x = 2(3) = 6.
If y = 3, then x = 3(4) = 12.
If y = 5, then x = 5(6) = 30.
If y = 7, then x = 7(8) = 56.

Now looking at the choices given, we see that 5x, 11x, 13x, and 57x could be the product of two consecutive integers when x equals 6, 12, 30, and 56, respectively. Therefore, only 23x could not be the product of two consecutive integers, because none of the values x could be is consecutive with 23.

Answer: D
_________________

Ans is D::23x


x= y(y+1) , y is prime nr <11 => 2,3,5,7 only can be values of y
x can be
2x3
3x4
5x6
7x8

A) 5x =>5x2x3 =6 => 5x6 consecutive
B) 11x=> 11x3x4=12 => 11x12 consecutive
C) 13x=> 13x3x4=12 => 13x12 or 12x13 consecutive
D) 23x=>23x3x4 =12 and 5x6=30 not possible
E). 57x=> 57x8x7 =56=> 56x57 consecutive

Clearly all values of x from Ato C and E are either 1 less of option or 1 more of option => Except the option D

Since x = y(y + 1) and y is a prime number less than 11, y = 2, 3, 5, or 7 and x = 6, 12, 30, or 56, respectively. As we can see, 5x, 11x, 13x, and 57x all can be the product of two consecutive integers. The only option that can’t is 23x since x is neither 22 nor 24.

Answer: D
_________________

GMATPrepNow What if y less than 13 would it be valid to eliminate D?
_________________

No it wouldn't.

If y = 11, then x = (11)(11 + 1) = 132

D) 23x
So, 23x = (23)(132) = 3036
3036 cannot be expressed as the product of 2 consecutive integers.
So, even if we allowed y to be 11, we still couldn't eliminate D

Cheers,
Brent

@Brent Thanks a lot Now I got it!!!
_________________

From the prompt we know that Y is a prime numbers that is less than 11 so 2,3,5, and 7.
When plugged into the original equation, we get the following answers for X:
(2)(2 +1)=6
(3) (3+1)= 12
(5) (5+1)= 30
(7) (7+1)= 56

From the next part of the prompt, we know we are looking for an answer that cannot be the product of two consecutive integers.
A) 5(6)- eliminate
B) 11(12)- eliminate
C 13 (12)- eliminate
D) 23x- keep
E) 57(56)- eliminate

D is the correct answer

Asked: If x = (y)(y + 1) and y is a prime number less than 11, which of the following could not be the product of 2 consecutive integers?


a) 5x = 5y(y+1): y=2; 5x = 5*6; Possible
b) 11x = 11y(y+1); y = 3; 11x = 11*12; Possible
c) 13x = 13y(y+1); y=3; 13x = 12*13; Possible
d) 23x = 23y(y+1); Not possible
e) 57x = 57y(y+1); y=7; 57x = 56*57; Possible

IMO D