Gruber's Essential Guide to Test Taking: Grades 6-9 - Gruber Gary R. 2019

Explanatory answers

Reading

1.(C) The story really describes the cleverness of Sally’s parachute.

This idea is present everywhere in the story and is the main theme of the story.

Wrong Choices:

(A)The Gold Pen only occurs marginally at the beginning of the story and end of the story and is not the focus of interest throughout the story.

(B)Certainly this was a strange contest, but that is not the chief element in the story—it is the parachute contraption that gets our interest.

(D)The strong breeze only occurred in one part of the story and although it might have been the cause of the cup turning, it is not the main attraction or theme of the story.

2.(C) Look at the wording in the story: “When Sally dropped hers, there was a strong breeze at the time, but the parachute opened smoothly. A little ways down, however, the plastic cup turned upside down...” The word however tells us that even though the parachute opened smoothly, the breeze later affected the cup.

Wrong Choices:

(A)Too small an egg would not make the cup turn over.

(B)The parachute opened smoothly but even if the parachute collapsed, due to the wind, it wouldn’t make the cup turn over. It would just make the cup go down faster.

(D)Cotton balls are so light that even if they were in the wrong place in the cup, they would not make the cup turn over.

3.(D) After her egg broke, the story says (in the last paragraph), Sally realized how to improve her contraption, and was excited to try again. She was also determined that she would win on the next try. This all indicates encouragement, not (A) surprise, or (B) anger or (C) sadness.

4.(D) The beginning of the story says that the principal was offering a gold pen to the winner.

Wrong Choices:

(A)Although students were dropping eggs, that wasn’t the prize.

(B)Although Sally used an old cloth for her parachute, that wasn’t the prize.

(C)Although Sally made a parachute, that wasn’t the prize.

Note that Choices A, B, and C try to lure the student who has superficially read the passage and casually just caught the words egg, cloth, parachute in the passage.

5.(C) Look at the third paragraph. It says that “Sally’s was by far the most interesting and promising.” This refers to Sally’s parachute contraption. Although the word promising can generally refer to Choices A, B, and D also, the word promising in the third paragraph cannot. Therefore Choices A, B, and D are incorrect.

6.(D) Although Sally was determined that she would win on the next try (last paragraph), this is an assumption and not a fact. Thus Choice D is correct.

Wrong Choices:

(A)It is a fact that the principal was offering a golden pen to the winner (beginning).

(B)It is a fact that nobody won the prize (see last paragraph).

(C)It is a fact that there was a strong breeze when Sally dropped her egg (see third paragraph).

You should realize that in many of these questions you have to be very exact in your analysis. You cannot base answers on your own assumptions or feelings, but must base them on what is in the story. For example, in question 3, although your feeling might have been one of anger when the egg broke, this was not Sally’s feeling. And it is Sally’s feeling that is asked for in the question.

Writing

1.(C)”. . . John is the worst soccer player.”

2.(C) “. . . he couldn’t find it anywhere.”

3.(C) “. . . we couldn’t decide where they came from” (they refers to coins).

4.(C) “You will see not only a beautiful sunset, but also see . . .”

5.(B) “John was so sure that he had arrived at school on time . . .” Use had to indicate the past of was.

6.(D) No error.

Vocabulary—Associate parts of words with prefixes or roots of words

1.(B) Think of PRE meaning “before.” Other words are predict, precursor, preceding.

2.(C) Think of MAL as “bad”. Other words are malevolent, malfunction, malware.

3.(D) Associate THERM with “Thermometer.” A thermometer measures heat.

4.(C) Think of the part TRANS meaning across as in transport or trans-continental. If you think IN mean “not” it seems that INTRANIGENT means that you can’t get something across. The closest choice is “not giving in” or “not compromising”.

5.(D) DE means “against” “away from”. LUD means to play. So DELUDE means to “play against”. The closest choice is D.

6.(C) The prefix in “misnomer” is “mis”. The prefix in “mislead” is “mis”. “Missle” and “Mystify” have no real prefix.

7.(A) Since PRO means forward or something that goes first, a “daughter” or “son” would fit.

8.(D) Choices A,B,C are always the case. However, IN can mean “not” as in INDECISIVE (not decisive) or “in” as in INJECT “throw in”.

9.(D) Since CIRCUMVENT means to come around, not go directly, Choice D is the best one.

10.(D) The prefix “de” mans away or against, so Choice D would be the best fit.

Math

1.(C) Use the strategy of multiplying the numerator and denominator by the same number to get a percent.

2.(C) or (D) Make it easy for yourself by working with simple numbers. 205 — 99 is the same as 206 — 100 since you’re adding 1 to both amounts here. Thus C is correct. Since 99 is 100 — 1, 205 — 99 is the same as 205 — 100 + 1 which is the same as Choice D.

3.(C) 3 hours + 4 hours = 7 hours. 20 minutes + 70 minutes = 90 minutes. So 7 hours + 90 minutes is your answer. There is no choice for that so we have to write 90 minutes in a different form. Write 90 minutes as 30 minutes + 60 minutes which is equal to 30 minutes + 1 hr. Thus 7 hours + 90 minutes = 8 hrs + 30 minutes.

4.(D) Write 5 ½ and 3 ½ in a different form. 5 1/2 = 11/2; 3 1/2 = 7/2. Thus 5 1/2 × 3 1/2 = 11/2 × 7/2 = 77/4 = 19 1/4

5.(A) If John gives 10 cards to Mary and 4 to Harry he has given 14 cards away. The remainder is 24 — 14 = 10. If he sells the remainder for 5cents 10 × 5 = 50 cents.

6.(B) Get a common denominator: 1/2 + 2/3 = 1/2 = 3/6, 2/3 = 4/6. So 1/2 + 2/3 = 3/6 + 4/6 = 7/6 = + 1/6.

7.(B) By reducing 25% to the fraction 1/4 we get, 25% of 160 = 1/4 × 160 = 40.

8.(C) Know what information to make use of. You want to find out how much Harry finally has. He starts with $15. He gives Mary $10 so he now has $5. Paul then gives Harry $2, so now Harry has $7.

9.(C) You would approximate 8.1 as 8 and 8.9 as 9. Then multiply 8 × 9 = 72.

10.(A) Try specific number like 3 and 5. 3 × 5 = 15. Add that to an even number, say 4, and you get 19, an odd number. However it may not always be even, so choose a different set of numbers. Say 7 and 11. You get 77, then add an even number, say 6. You get 83 an odd number. So I would venture that Choice A is correct.

In general you should know that an odd number times an odd number is odd and when an odd number is added to an even number you get an odd number.

11.(C) Write the number as N. So you get 2/3 × N = 6. Multiply both sides of the equality by 3 to get rid of the fraction. You get: 2 × N = 6 × 3. 2 × N = 18. Now divide by 2: You get N = 9.

12.(B) You have to realize that every complete rotation, that is 0 to 0, $4 comes out. So we divide $173 by 4 and we get 43 1/4. That means there was 43 complete revolutions and 1/4 left. Thus the hand must be point to the 1.

13.(C) You translate is to 5, what to x, of to × (times) and percent to /100. = is what percent of 10 becomes 5 = x/100 × 10, or 5 = x/100 × 10. So, 5 = x (10/100); 5 = x/10 and so 50 = x.

14.(B) You write a proportion:

or

1/6 = 2 1/2/x

Cross multiply: x × + = 6 × 2 1/2 = 6 × 5/2 x = 15

15.(B) The area of the shaded region is found by subtracting the area of the large circle from the area of the small circle. Thus, the area of the shaded region is just 20 — 12 = 8 (Choice B).

16.(D) Label CD = 5 (since CD = BC) and ED = 8 (since ED = AE). This makes the perimeter 8 + 8 + = + = + 14 = 40 (Choice D).

17.What you want to know is what section of the graph looks as if it is 60% of the total graph (total cost). You can see that “Other Vegetables” make up a block that is about three fifths, or 60% of the total. All of the other sections make up less than one half (50 percent) of the total.

18.Translate words into math:

19.Translate words into math:

20.Translate words into math:

Call the number of boys b. Now translate:

The ratio of boys to girls is 3 to 4:

Something you may want to note: Since it was stated that the ratio of boys to girls was 3 to 4, there must be fewer boys than girls. So there must be less than 24 boys because there are 24 girls. You can therefore rule out Choices C and D immediately.