BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

A collection of 36 cards consists of 4 sets of 9 cards in

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Legendary Member
Posts: 2898
Joined: Thu Sep 07, 2017 2:49 pm
Thanked: 6 times
Followed by:5 members

A collection of 36 cards consists of 4 sets of 9 cards in

by Vincen » Sat Nov 30, 2019 7:30 am
A collection of 36 cards consists of 4 sets of 9 cards in each set are numbered 1 through 9. If one card has been removed from the collection, what is the number on that card?

(1) The units digit of the sum of the numbers on the remaining 35 cards is 6.
(2) The sum of the numbers on the remaining 35 cards is 176.

[spoiler]OA=D[/spoiler]

Source: Official Guide
Top
Source: — Data Sufficiency |
Legendary Member
Posts: 2214
Joined: Fri Mar 02, 2018 2:22 pm
Followed by:5 members

by deloitte247 » Sun Dec 01, 2019 6:25 am
Given that;
1 collection = 36 cards
36 cards = 4 sets at 9 card per set
Each set contains cards that are numbered 1-9

Question => what is the number on the card that was removed?

Statement 1 => The units digit of the sum of the numbers on the remaining 35 cards is 6
Sum of digits on all 9 cards = 1 +2 +3 +4 +5 +6 +7 +8 +9 = 45
Sum for all the 4 set = 4 * 45 = 180
When one card is removed, sum of the remaining 35 cards has the last digit to be = 6
180 - 1 = 179, 180 - 2 = 178, 180 - 3 = 177, 180 - 4 = 176, 180 - 5 = 175, 180 - 6 = 174
180 - 7 = 173, 180 - 8 = 172, 180 - 9 = 171
180 - 4 = 176 is the only card that will have the sum of the remaining 35 cards to be = 176 (with the last digit as 6)
Hence, number on the card removed = 4 ; statement 1 is SUFFICIENT

Statement 2 => The sum of the numbers on the remaining 35 cards is 176
Sum of digits on all 9 cards = 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 +9 = 45
Sum of all the 4 sets = 4 * 45 = 180
From this statement 2 => 180 - (value of chosen card) = 176
180 - 176 = value of chosen card
chosen card = 4
Statement 2 is SUFFICIENT

Since each statement alone is SUFFICIENT
Answer = option D
Top

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 16207
Joined: Mon Dec 08, 2008 6:26 pm
Location: Vancouver, BC
Thanked: 5254 times
Followed by:1268 members
GMAT Score:770

by Brent@GMATPrepNow » Sun Dec 01, 2019 6:42 am
Vincen wrote:A collection of 36 cards consists of 4 sets of 9 cards in each set are numbered 1 through 9. If one card has been removed from the collection, what is the number on that card?

(1) The units digit of the sum of the numbers on the remaining 35 cards is 6.
(2) The sum of the numbers on the remaining 35 cards is 176.

[spoiler]OA=D[/spoiler]

Source: Official Guide
Target question: What is the number on the card?

Given: A collection of 36 cards consists of 4 sets of 9 cards in each set are numbered 1 through 9.

Statement 1: The units digit of the sum of the numbers on the remaining 35 cards is 6.
1+2+3+4+5+6+7+8+9=45
Since there are 4 sets of cards numbered 1 to 9, the SUM of all 36 cards = 4(45) = 180

When we remove one card, the sum of the REMAINING 35 cards = --6 (units digit 6)
In other words, 180 - (value of chosen card) = --6
So, the value of the chosen card must be 4
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: The sum of the numbers on the remaining 35 cards is 176.
In other words, 180 - (value of chosen card) = 176
So, the value of the chosen card must be 4
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer: D

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
Image
Top
Post new topic Post Reply
• Page 1 of 1