If 23^3*19^4*14^2 = x, what is the units digit of x ?

Question

If 23^3*19^4*14^2 = x, what is the units digit of x ?
 
A. 2
B. 3
C. 6
D. 7
E. 9

Skywalker18 · Answer

23^3*19^4*14^2 = x

Units digit of x will be 
3^3 * 9^4 * 4^2
=7* 1 *6
=42

Therefore , units digit of x = 2

Answer A

BrentGMATPrepNow · Answer

Two comments: 1) If you were pressed for time, you might recognize that 14^2 is an EVEN number, which means the entire product must be EVEN. When we check the answer choices, we see that 3 of them indicate ODD numbers, so we can ELIMINATE B, D and E. At this point, you have a 50-50 chance of guessing correctly. 2) The powers in this question aren't huge. However, if they were larger, you can use the strategies shown in this free video - https://www.gmatprepnow.com/module/gmat- ... video/1031 Afterward, you can practice with this question - https://www.gmatprepnow.com/module/gmat- ... video/1032 Cheers, Brent

EMPOWERgmatRichC · Answer

Hi All,

We're told that X = (23^3)(19^4)(14^2). We're asked for the unit's digit (re: the "ones digit") of X. While this question might look a little 'scary' it involves some Number Property rules that you can take advantage of and you really just need to do some basic multiplication to answer the question.

To start, 'squaring' an EVEN number will get us an EVEN number. So 14^2 is EVEN. Next, any time you multiply an integer by an EVEN number, the product will also be EVEN. Here, we're multiplying 3 integers together - and we already know that 14^2 is EVEN, so the value of X will also be EVEN. This means that the units digit of X must be an EVEN number (0, 2, 4, 6 or 8). At this point, we can eliminate Answers B, D and E.

To find the units digit of a number, we just have to multiply the units digits of the products together...

14^2 = (14)(14).... here, the product of the units digits is (4)(4)..... 16..... the units digit of the end product is 6 
23^3 = (23)(23)(23).... here, the product of the units digits is (3)(3)(3)..... 27..... the units digit of the end product is 7 
19^4 = (19)(19)(19)(19).... here, the product of the units digits is (9)(9)(9)(9)..... 6561..... the units digit of the end product is 1

Multiplying those three units digits together, we get (6)(7)(1) = 42... so the units digit of X is 2.

Final Answer:  A

GMAT assassins aren't born, they're made, 
Rich

If 23^319^414^2 = x, what is the units digit of x ?

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