GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 19 Oct 2019, 07:56

Close

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

In the multiplication problem above, F, G, and H represent unique odd

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Find Similar Topics 
Senior RC Moderator
User avatar
V
Joined: 02 Nov 2016
Posts: 4117
GPA: 3.39
In the multiplication problem above, F, G, and H represent unique odd  [#permalink]

Show Tags

New post 14 Mar 2017, 10:10
3
1
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

69% (02:09) correct 31% (01:54) wrong based on 106 sessions

HideShow timer Statistics

In the multiplication problem below, F, G, and H represent unique odd digits. What is the value of the three-digit number FGF?

(A) 151
(B) 161
(C) 171
(D) 313
(E) 353

Attachments

123.jpg
123.jpg [ 2.88 KiB | Viewed 1463 times ]


_________________
Current Student
avatar
V
Joined: 28 May 2014
Posts: 515
GMAT 1: 730 Q49 V41
GMAT ToolKit User
Re: In the multiplication problem above, F, G, and H represent unique odd  [#permalink]

Show Tags

New post 14 Mar 2017, 12:02
FGF
x G
----
HGG

Now, (C) and (E) are out because they provide 4 digits number after multiplication(17 x 7 = 119; 35 x 5 = 105).

(D) is out because for (D) : FGF = HGG; (313 x 1 = 313)

For (B) : 161 x 6 = 966 (FGF x G = HGG - Satisfied)
For (A) : 151 x 5 = 755 (FGF x G = HGG - Satisfied)

Both A & B can be the answer.
_________________
Magoosh GMAT Instructor
User avatar
G
Joined: 28 Dec 2011
Posts: 4472
Re: In the multiplication problem above, F, G, and H represent unique odd  [#permalink]

Show Tags

New post 14 Mar 2017, 12:11
1
SajjadAhmad wrote:
In the multiplication problem below, F, G, and H represent unique odd digits. What is the value of the three-digit number FGF?

(A) 151
(B) 161
(C) 171
(D) 313
(E) 353

Dear SajjadAhmad,

I'm happy to respond. :-)

First, notice that F x G has to be G, or at least has to have a units digit of G. The three with F = 1 all work.

For (D), it's true that F x G = G, but of course 313 x 1 = 313, and this doesn't fit the pattern. (D) is incorrect.

For (E), F x G = 15, which has a units digit of G = 5. Notice, though, that 5 x 300 = 1500, so 5 x 353 > 1500, and this is NOT a three-digit number. (E) is incorrect.

In fact, 17 x 7 = 119, so 170 x 7 = 1190, and 171 x 7 = 1197, also not a three-digit number. (C) is incorrect.

That leaves us with (A) & (B). Both fit the digits pattern, but notice that the prompt specifies that F, G, and H are unique ODD digits. Thus, (B) is out, because one of its digits is the even number 6.

That leaves (A). OA = (A)

We never had to do the calculation, but it's not hard:
15 x 5 = 75
so 150 x 5 = 750
so 151 x 5 = 755

Does all this make sense?
Mike :-)
_________________
Mike McGarry
Magoosh Test Prep


Education is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)
Director
Director
avatar
G
Joined: 02 Sep 2016
Posts: 649
Re: In the multiplication problem above, F, G, and H represent unique odd  [#permalink]

Show Tags

New post 03 Apr 2017, 04:26
Bunuel and mikemcgarry

I solved it using this approach. It would be great if you could give your insights on this.

F,G, and H are odd DIGITS. Therefore they can only take values 1,3,5,7, and 9.

F*G= G
That is possible in two cases:
(1) If both (F and G) are 1.
(2) If one of the two is 1 and that would be F.
(3) If both are 5 (5*5=5) but in this case we would not get 5 at tens place as there will be a carryover. (So cancelled)

Therefore D and E eliminated.

We are left with 151, 161, and 171.

FGF*G= HGG

F*G= G (no carryover)
G*G= G
Therefore G ends in 5 or 6 (because 5*5=ends in 5 and 6*6= ends in 6)
But we are told that the digits are even. Therefore 161 is eliminated.
171 is not the answer because 7*7= ends in 9 and not 7.

The answer thus is 151.
_________________
Help me make my explanation better by providing a logical feedback.

If you liked the post, HIT KUDOS !!

Don't quit.............Do it.
Magoosh GMAT Instructor
User avatar
G
Joined: 28 Dec 2011
Posts: 4472
Re: In the multiplication problem above, F, G, and H represent unique odd  [#permalink]

Show Tags

New post 15 May 2017, 13:28
1
Shiv2016 wrote:
Bunuel and mikemcgarry

I solved it using this approach. It would be great if you could give your insights on this.

F,G, and H are odd DIGITS. Therefore they can only take values 1,3,5,7, and 9.

F*G= G
That is possible in two cases:
(1) If both (F and G) are 1.
(2) If one of the two is 1 and that would be F.
(3) If both are 5 (5*5=5) but in this case we would not get 5 at tens place as there will be a carryover. (So cancelled)

Therefore D and E eliminated.

We are left with 151, 161, and 171.

FGF*G= HGG

F*G= G (no carryover)
G*G= G
Therefore G ends in 5 or 6 (because 5*5=ends in 5 and 6*6= ends in 6)
But we are told that the digits are even. Therefore 161 is eliminated.
171 is not the answer because 7*7= ends in 9 and not 7.

The answer thus is 151.

Dear Shiv2016,

I'm happy to respond. :-)

I have some thoughts about how you started. You suggested F = G = 1 or F = G = 5, but the problem states quite clearly that all three numbers are unique, i.e. distinct. Thus, we cannot have repeats.

Also, you assumed that F*G = G. You over looked the possibility that F*G is a two digit number with a last digit of G. For example, if G = 5, then F could be any odd number, and the unit digit of the product will be 5. As it happens, we get no answer choices of that sort, but given the stem, theoretically, the answer could have been in that form, and your approach would have missed it.

My friend, does all this make sense?
Mike :-)
_________________
Mike McGarry
Magoosh Test Prep


Education is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)
Manager
Manager
User avatar
S
Joined: 02 May 2016
Posts: 75
Location: India
Concentration: Entrepreneurship
GRE 1: Q163 V154
WE: Information Technology (Computer Software)
Reviews Badge
Re: In the multiplication problem above, F, G, and H represent unique odd  [#permalink]

Show Tags

New post 17 Jun 2017, 05:24
saswata4s wrote:
FGF
x G
----
HGG

Now, (C) and (E) are out because they provide 4 digits number after multiplication(17 x 7 = 119; 35 x 5 = 105).

(D) is out because for (D) : FGF = HGG; (313 x 1 = 313)

For (B) : 161 x 6 = 966 (FGF x G = HGG - Satisfied)
For (A) : 151 x 5 = 755 (FGF x G = HGG - Satisfied)

Both A & B can be the answer.


Question says digits are odd. But B has 6 which is even, so it is out.
So A is the answer :)
Senior RC Moderator
User avatar
V
Joined: 02 Nov 2016
Posts: 4117
GPA: 3.39
Re: In the multiplication problem above, F, G, and H represent unique odd  [#permalink]

Show Tags

New post 21 Feb 2019, 11:25
Official Explanation


At first it looks as though you’ll have to substitute every odd digit for the three variables until you stumble onto the correct answer, but there’s a trick to this problem that eliminates such guesswork. Look at the units column of the problem and you’ll see that F × G yields a product with a units digit of G; therefore, it is quite possible that F is

1. Actually, you can go even further: F must equal 1, because G cannot equal 1 (otherwise, the product of this multiplication problem would be FGF, not HGG). Plus, if both F and G were odd digits greater than 1, the product of this multiplication problem would be a four-digit number. Because the product is the three-digit number HGG, F equals 1. You can now eliminate (D) and (E), and you also know that G must equal 5 or 7 (G cannot equal 6 because the problem says G must be an odd digit). When G equals 7, the product is a four digit number; therefore, G is 5, and the correct answer is (A). But you could have just plugged the answer choices into the problem, one at a time, to see which one works


Hope it Helps
_________________
GMAT Club Bot
Re: In the multiplication problem above, F, G, and H represent unique odd   [#permalink] 21 Feb 2019, 11:25
Display posts from previous: Sort by

In the multiplication problem above, F, G, and H represent unique odd

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  





Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne