- Jake has twice as many marbles as Lisa. Lisa has 3 more marbles than Tom. If Tom has 4 marbles, how many marbles does Jake have?
Answer: 14 marbles
Tom has 4 marbles. Lisa has 3 more than Tom, so Lisa has 4 + 3 = 7 marbles. Jake has twice as many as Lisa, so Jake has 2 × 7 = 14 marbles. Choice A (10) incorrectly calculates 2 × (4 + 1). Choice B (11) adds all the numbers incorrectly. Choice D (22) incorrectly calculates 2 × (4 + 3 + 4).
- Sam counts by 2s starting from 4: 4, 6, 8, 10, 12... Maya counts by 3s starting from 3: 3, 6, 9, 12, 15... What is the third number that both children will say?
Answer: 18
Both sequences share: 6 (first), 12 (second), and 18 (third). Sam's sequence: 4, 6, 8, 10, 12, 14, 16, 18... Maya's sequence: 3, 6, 9, 12, 15, 18... Choice B (20) appears in Sam's sequence but not Maya's. Choice C (24) is the fourth common number. Choice D (30) is the fifth common number.
- In a box, there are 15 red balls and some blue balls. There are 4 fewer blue balls than red balls. How many balls are in the box altogether?
Answer: 26 balls total
When you see word problems with phrases like "fewer than" or "more than," you're working with comparison relationships. The key is to identify what you know and what you need to find, then work step by step.
You know there are 15 red balls, and the blue balls are "4 fewer than red balls." This means you subtract 4 from the number of red balls: 15−4=11 blue balls. Now you can find the total by adding red and blue balls together: 15+11=26 balls altogether.
Let's see why the other answers are wrong. Choice A (19 balls) happens when students mistakenly add 4 to the red balls instead of subtracting: 15+4=19. This misinterprets "4 fewer" as "4 more." Choice B (30 balls) occurs when students double the red balls (15×2=30), perhaps confusing this with a different type of problem. Choice D (34 balls) results from adding both the red balls and the "4 fewer" incorrectly: 15+15+4=34, treating the 4 as an addition rather than understanding it describes the difference.
When you encounter "fewer than" or "less than" problems, always subtract from the reference number. Circle key phrases like "fewer than" and underline what you're comparing it to. This helps you avoid the common trap of adding when you should subtract. - Look at this subtraction: 23 - __ = 15. Now use that missing number in this addition: 7 + __ = ?. What is the final answer?
Answer: 15
First find the missing number: 23 - __ = 15, so the missing number is 23 - 15 = 8. Then use 8 in the addition: 7 + 8 = 15. Choice A (13) incorrectly uses 23 - 15 = 8 as the final answer but subtracts 2. Choice C (17) adds 23 - 15 + 7 + 2 incorrectly. Choice D (22) adds 15 + 7 incorrectly.
- Look at this pattern: 3, 6, 4, 7, 5, 8, ?, ?. What are the next two numbers?
Answer: 6 and 9
This is two alternating patterns: starting positions (3, 4, 5, 6...) add 1 each time, and even positions (6, 7, 8, 9...) also add 1 each time. So the 7th number is 6 and the 8th number is 9. Choice B adds 2 to the even position incorrectly. Choice C uses 7 from the wrong position. Choice D reverses the correct order.
- Anna saves $2 each week. After 4 weeks, she spends $3 on a toy. Then she saves for 2 more weeks. How much money does Anna have now?
Answer: $9 left over
This is a multi-step word problem that requires you to track Anna's money over time, following each saving and spending action in order.
Let's work through Anna's money step by step. She saves $2 each week for 4 weeks, so she has 2×4=8 dollars. Then she spends $3 on a toy, leaving her with 8−3=5 dollars. After that, she saves $2 per week for 2 more weeks, adding 2×2=4 more dollars. Her final total is 5+4=9 dollars.
Looking at the wrong answers: Choice A ($5) represents only the amount Anna had right after buying the toy, but ignores the additional 2 weeks of saving afterward. Choice B ($13) likely comes from adding all her savings without subtracting what she spent: 2×6=12 dollars saved total, plus maybe an arithmetic error. Choice C ($11) might result from calculating 2×4+2×2−3=8+4−3=9 but making an error in the final subtraction, or from adding the spent money instead of subtracting it.
When solving multi-step word problems, always work chronologically through each action. Write down what happens at each step rather than trying to do all the math at once. This helps you avoid mixing up the order of operations and ensures you don't skip any steps in the problem. - Ben arranges blocks in groups. Group 1 has 2 blocks. Group 2 has 5 blocks. Group 3 has 8 blocks. Group 4 has 11 blocks. If this pattern continues, how many blocks will be in Groups 5 and 6 combined?
Answer: 31 blocks combined
When you see a question about number patterns, look for what changes from one group to the next. This helps you find the rule that governs the sequence.
Let's examine how many blocks are added each time: Group 1 has 2 blocks, Group 2 has 5 blocks (that's 3 more), Group 3 has 8 blocks (3 more again), and Group 4 has 11 blocks (3 more once again). The pattern adds 3 blocks to each new group.
Following this rule: Group 5 = 11 + 3 = 14 blocks, and Group 6 = 14 + 3 = 17 blocks. Combined, Groups 5 and 6 have 14 + 17 = 31 blocks.
Answer choice A (28 blocks) likely comes from miscounting the pattern as adding only 2 blocks each time instead of 3. Answer choice B (35 blocks) might result from incorrectly thinking the pattern adds 4 blocks each time, or from calculation errors. Answer choice C (33 blocks) could happen if you correctly found Group 5 has 14 blocks but mistakenly calculated Group 6 as having 19 blocks instead of 17.
The correct answer is D (31 blocks combined).
For pattern questions like this, always write out the differences between consecutive terms first. Once you identify that consistent difference, you can confidently extend the pattern. Double-check your arithmetic, especially when combining final answers, since small calculation mistakes can lead you to tempting wrong choices.
- Emma has 8 stickers. She gives away some stickers and then gets 3 more from her friend. Now she has 7 stickers. How many stickers did Emma give away?
Answer: 4 stickers
Working backwards: Emma ended with 7 stickers after getting 3 more, so before getting the 3 stickers she had 7 - 3 = 4 stickers. She started with 8 stickers and had 4 left after giving some away, so she gave away 8 - 4 = 4 stickers. Choice A (2) is the difference between final and starting amounts. Choice C (5) comes from incorrectly adding 8 + 3 - 7. Choice D (6) comes from subtracting 7 - 1 instead of proper calculation.
